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Keywords = integral formula

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17 pages, 1651 KiB  
Article
A Comprehensive User Acceptance Evaluation Framework of Intelligent Driving Based on Subjective and Objective Integration—From the Perspective of Value Engineering
by Wang Zhang, Fuquan Zhao, Zongwei Liu, Haokun Song and Guangyu Zhu
Systems 2025, 13(8), 653; https://doi.org/10.3390/systems13080653 (registering DOI) - 2 Aug 2025
Abstract
Intelligent driving technology is expected to reshape urban transportation, but its promotion is hindered by user acceptance challenges and diverse technical routes. This study proposes a comprehensive user acceptance evaluation framework for intelligent driving from the perspective of value engineering (VE). The novelty [...] Read more.
Intelligent driving technology is expected to reshape urban transportation, but its promotion is hindered by user acceptance challenges and diverse technical routes. This study proposes a comprehensive user acceptance evaluation framework for intelligent driving from the perspective of value engineering (VE). The novelty of this framework lies in three aspects: (1) It unifies behavioral theory and utility theory under the value engineering framework, and it extracts key indicators such as safety, travel efficiency, trust, comfort, and cost, thus addressing the issue of the lack of integration between subjective and objective factors in previous studies. (2) It establishes a systematic mapping mechanism from technical solutions to evaluation indicators, filling the gap of insufficient targeting at different technical routes in the existing literature. (3) It quantifies acceptance differences via VE’s core formula of V = F/C, overcoming the ambiguity of non-technical evaluation in prior research. A case study comparing single-vehicle intelligence vs. collaborative intelligence and different sensor combinations (vision-only, map fusion, and lidar fusion) shows that collaborative intelligence and vision-based solutions offer higher comprehensive acceptance due to balanced functionality and cost. This framework guides enterprises in technical strategy planning and assists governments in formulating industrial policies by quantifying acceptance differences across technical routes. Full article
(This article belongs to the Special Issue Modeling, Planning and Management of Sustainable Transport Systems)
23 pages, 2554 KiB  
Article
Modeling the Higher Heating Value of Spanish Biomass via Neural Networks and Analytical Equations
by Anbarasan Jayapal, Fernando Ordonez Morales, Muhammad Ishtiaq, Se Yun Kim and Nagireddy Gari Subba Reddy
Energies 2025, 18(15), 4067; https://doi.org/10.3390/en18154067 (registering DOI) - 31 Jul 2025
Abstract
Accurate estimation of biomass higher heating value (HHV) is crucial for designing efficient bioenergy systems. In this study, we developed a Backpropagation artificial neural network (ANN) that predicts HHV from routine proximate/ultimate composition data. The network (9-6-6-1 architecture, trained for 15,000 epochs with [...] Read more.
Accurate estimation of biomass higher heating value (HHV) is crucial for designing efficient bioenergy systems. In this study, we developed a Backpropagation artificial neural network (ANN) that predicts HHV from routine proximate/ultimate composition data. The network (9-6-6-1 architecture, trained for 15,000 epochs with learning rate 0.3 and momentum 0.4) was calibrated on 99 diverse Spanish biomass samples (inputs: moisture, ash, volatile matter, fixed carbon, C, H, O, N, S). The optimized ANN achieved strong predictive accuracy (validation R2 ≈ 0.81; mean squared error ≈ 1.33 MJ/kg; MAE ≈ 0.77 MJ/kg), representing a substantial improvement over 54 analytical models despite the known complexity and variability of biomass composition. Importantly, in direct comparisons it significantly outperformed 54 published analytical HHV correlations—the ANN achieved substantially higher R2 and lower prediction error than any fixed-form formula in the literature. A sensitivity analysis confirmed chemically intuitive trends (higher C/H/FC increase HHV; higher moisture/ash/O reduce it), indicating the model learned meaningful fuel-property relationships. The ANN thus provided a computationally efficient and robust tool for rapid, accurate HHV estimation from compositional data. Future work will expand the dataset, incorporate thermal pretreatment effects, and integrate the model into a user-friendly decision-support platform for bioenergy applications. Full article
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17 pages, 539 KiB  
Article
Non-Fragile H Asynchronous State Estimation for Delayed Markovian Jumping NNs with Stochastic Disturbance
by Lan Wang, Juping Tang, Qiang Li, Xianwei Yang and Haiyang Zhang
Mathematics 2025, 13(15), 2452; https://doi.org/10.3390/math13152452 - 30 Jul 2025
Viewed by 104
Abstract
This article focuses on tackling the non-fragile H asynchronous estimation problem for delayed Markovian jumping neural networks (NNs) featuring stochastic disturbance. To more accurately reflect real-world scenarios, external random disturbances with known statistical characteristics are incorporated. Through the integration of stochastic analysis [...] Read more.
This article focuses on tackling the non-fragile H asynchronous estimation problem for delayed Markovian jumping neural networks (NNs) featuring stochastic disturbance. To more accurately reflect real-world scenarios, external random disturbances with known statistical characteristics are incorporated. Through the integration of stochastic analysis theory and Lyapunov stability techniques, as well as several matrix constraints formulas, some sufficient and effective results are addressed. These criteria ensure that the considered NNs achieve anticipant H stability in line with an external disturbance mitigation level. Meanwhile, the expected estimator gains will be explicitly constructed by dealing with corresponding matrix constraints. To conclude, a numerical simulation example is offered to showcase workability and validity of the formulated estimation method. Full article
(This article belongs to the Special Issue Advanced Filtering and Control Methods for Stochastic Systems)
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17 pages, 2979 KiB  
Article
Discussion on the Design of Sprayed Eco-Protection for Near-Slope Roads Along Multi-Level Slopes
by Haonan Chen and Jianjun Ye
Appl. Sci. 2025, 15(15), 8408; https://doi.org/10.3390/app15158408 - 29 Jul 2025
Viewed by 88
Abstract
This study proposes a design method for near-slope roads along multi-level slopes that integrates excavation requirements and post-construction ecological restoration through sprayed eco-protection. Firstly, the design principles and procedural steps for near-slope roads are established. The planar layouts of multi-level slopes are categorized, [...] Read more.
This study proposes a design method for near-slope roads along multi-level slopes that integrates excavation requirements and post-construction ecological restoration through sprayed eco-protection. Firstly, the design principles and procedural steps for near-slope roads are established. The planar layouts of multi-level slopes are categorized, including mixing areas, turnaround areas, berms, and access ramps. Critical technical parameters, such as curve radii and widths of berms and ramps, as well as dimensional specifications for turnaround areas, are systematically formulated with corresponding design formulas. The methodology is applied to the ecological restoration project of multi-level slopes in the Huamahu mountainous area, and a comparative technical-economic analysis is conducted between the proposed design and the original scheme. Results demonstrate that the optimized design reduces additional maintenance costs caused by near-slope roads by 6.5–8.0% during the curing period. This research advances the technical framework for multi-level slope governance and enhances the ecological design standards for slope protection engineering. Full article
(This article belongs to the Section Earth Sciences)
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48 pages, 1213 KiB  
Article
Parameterized Fractal–Fractional Analysis of Ostrowski- and Simpson-Type Inequalities with Applications
by Saad Ihsan Butt, Muhammad Mehtab and Youngsoo Seol
Fractal Fract. 2025, 9(8), 494; https://doi.org/10.3390/fractalfract9080494 - 28 Jul 2025
Viewed by 114
Abstract
In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. [...] Read more.
In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski- and Simpson-type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical Hölder and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of Hölder and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis. Full article
(This article belongs to the Section General Mathematics, Analysis)
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25 pages, 8335 KiB  
Article
Integrative In Silico and In Vivo Analysis of Banhasasim-Tang for Irritable Bowel Syndrome: Mechanistic Insights into Inflammation-Related Pathways
by Woo-Gyun Choi, Seok-Jae Ko, Jung-Ha Shim, Chang-Hwan Bae, Seungtae Kim, Jae-Woo Park and Byung-Joo Kim
Pharmaceuticals 2025, 18(8), 1123; https://doi.org/10.3390/ph18081123 - 27 Jul 2025
Viewed by 375
Abstract
Background/Objectives: Banhasasim-tang (BHSST) is a traditional herbal formula commonly used to treat gastrointestinal (GI) disorders and has been considered a potential therapeutic option for irritable bowel syndrome (IBS). This study aimed to explore the molecular targets and underlying mechanisms of BHSST in IBS [...] Read more.
Background/Objectives: Banhasasim-tang (BHSST) is a traditional herbal formula commonly used to treat gastrointestinal (GI) disorders and has been considered a potential therapeutic option for irritable bowel syndrome (IBS). This study aimed to explore the molecular targets and underlying mechanisms of BHSST in IBS using a combination of network pharmacology, molecular docking, molecular dynamics simulations, and in vivo validation. Methods: Active compounds in BHSST were screened based on drug-likeness and oral bioavailability. Potential targets were predicted using ChEMBL, and IBS-related targets were obtained from GeneCards and DisGeNET. A compound–target–disease network was constructed and analyzed via Gene Ontology and KEGG pathway enrichment. Compound–target interactions were further assessed using molecular docking and molecular dynamics simulations. The in vivo effects of eudesm-4(14)-en-11-ol, elemol, and BHSST were evaluated in a zymosan-induced IBS mouse model. Results: Twelve BHSST-related targets were associated with IBS, with enrichment analysis identifying TNF signaling and apoptosis as key pathways. In silico simulations suggested stable binding of eudesm-4(14)-en-11-ol to TNF-α and kanzonol T to PIK3CD, whereas elemol showed weak interaction with PRKCD. In vivo, eudesm-4(14)-en-11-ol improved colon length, weight, stool consistency, TNF-α levels, and pain-related behaviors—effects comparable to those of BHSST. Elemol, however, showed no therapeutic benefit. Conclusions: These findings provide preliminary mechanistic insight into the anti-inflammatory potential of BHSST in IBS. The integrated in silico and in vivo approaches support the contribution of specific components, such as eudesm-4(14)-en-11-ol, to its observed effects, warranting further investigation. Full article
(This article belongs to the Special Issue Network Pharmacology of Natural Products, 2nd Edition)
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31 pages, 2472 KiB  
Article
Increase in Grain Production Potential of China Under 2030 Well-Facilitated Farmland Construction Goal
by Jianya Zhao, Fanhao Yang, Yanglan Zhang and Shu Wang
Land 2025, 14(8), 1538; https://doi.org/10.3390/land14081538 - 27 Jul 2025
Viewed by 334
Abstract
To promote high-quality agricultural development and implement the “storing grain in the land” strategy, the construction of Well-Facilitated Farmland (WFF) plays a critical role in enhancing grain production capacity and optimizing the spatial distribution of food supply, thereby contributing to national food security. [...] Read more.
To promote high-quality agricultural development and implement the “storing grain in the land” strategy, the construction of Well-Facilitated Farmland (WFF) plays a critical role in enhancing grain production capacity and optimizing the spatial distribution of food supply, thereby contributing to national food security. However, accurately assessing the potential impact of WFF construction on China’s grain production and regional self-sufficiency by 2030 remains a significant challenge. Existing studies predominantly focus on the provincial level, while fine-grained analyses at the city level are still lacking. This study quantifies the potential increase in grain production in China under the 2030 WFF construction target by employing effect size analysis, multi-weight prediction, and Monte Carlo simulation across multiple spatial scales (national, provincial, and city levels), thereby addressing the research gap at finer spatial resolutions. By integrating 2030 population projections and applying a grain self-sufficiency calculation formula, it further evaluates the contribution of WFF to regional grain self-sufficiency: (1) WFF could generate an additional 31–48 million tons of grain, representing a 5.26–8.25% increase; (2) grain supply in major crop-producing regions would expand, while the supply–demand gap in balanced regions would narrow; and (3) the number of cities with grain self-sufficiency ratios below 50% would decrease by 11.1%, while those exceeding 200% would increase by 25.5%. These findings indicate that WFF construction not only enhances overall grain production potential but also facilitates a transition from “overall supply-demand balance” to “structural security” within China’s food system. This study provides critical data support and policy insights for building a more resilient and regionally adaptive agricultural system. Full article
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42 pages, 667 KiB  
Article
Canaanite Literary Culture Before the Bible, a View from the Canaanite Amarna Letters
by Alice Mandell
Religions 2025, 16(8), 970; https://doi.org/10.3390/rel16080970 - 26 Jul 2025
Viewed by 350
Abstract
The present study highlights how the Canaanite Amarna Letters offer unique insight into Canaanite literary culture in the Late Bronze Age. The letters represent the diplomatic acumen of scribes writing letters for local elites that were sent to the Egyptian court in the [...] Read more.
The present study highlights how the Canaanite Amarna Letters offer unique insight into Canaanite literary culture in the Late Bronze Age. The letters represent the diplomatic acumen of scribes writing letters for local elites that were sent to the Egyptian court in the mid-fourteenth century BCE. Yet they also preserve the earliest evidence of Canaanite literary forms and compositional practices. The letters include memorized formulae and expressions, word pairs, poetic devices, and the use of repetition to frame poetic units, which are common in the practices of later first-millennium scribes working in this same region, including those who wrote the Hebrew Bible. The letters also offer insight into the ways that the scribes combined memorized units into new narrative contexts. Such features added literary texture to the letters, but also contributed to their rhetorical aims. While some poetic passages in the letters may be novel compositions, there is also evidence that literary forms and expressions were integral to Canaanite scribal education by the Amarna period. The Canaanite Letters therefore set an important precedent for literary creation, and for the scribes’ bricolage practices in the process of creating new diplomatic letters. Full article
(This article belongs to the Special Issue The Bible and Ancient Mesopotamia)
23 pages, 4079 KiB  
Article
Investigation on the Bearing Characteristics and Bearing Capacity Calculation Method of the Interface of Reinforced Soil with Waste Tire Grid
by Jie Sun, Yuchen Tao, Zhikun Liu, Xiuguang Song, Wentong Wang and Hongbo Zhang
Buildings 2025, 15(15), 2634; https://doi.org/10.3390/buildings15152634 - 25 Jul 2025
Viewed by 232
Abstract
Geogrids are frequently utilized in engineering for reinforcement; yet, they are vulnerable to construction damage when employed on coarse-grained soil subgrades. In contrast, waste tire grids are more appropriate for subgrade reinforcement owing to their rough surfaces, integrated steel meshes, robust transverse ribs, [...] Read more.
Geogrids are frequently utilized in engineering for reinforcement; yet, they are vulnerable to construction damage when employed on coarse-grained soil subgrades. In contrast, waste tire grids are more appropriate for subgrade reinforcement owing to their rough surfaces, integrated steel meshes, robust transverse ribs, extended degradation cycles, and superior durability. Based on the limit equilibrium theory, this study developed formulae for calculating the internal and external frictional resistance, as well as the end resistance of waste tires, to ascertain the interface bearing properties and calculation techniques of waste tire grids. Based on this, a mechanical model for the ultimate pull-out resistance of waste-tire-reinforced soil was developed, and its validity was confirmed through a series of pull-out tests on single-sided strips, double-sided strips, and tire grids. The results indicated that the tensile strength of one side of the strip was approximately 43% of that of both sides, and the rough outer surface of the tire significantly enhanced the tensile performance of the strip; under identical normal stress, the tensile strength of the single-sided tire grid was roughly nine times and four times greater than that of the single-sided and double-sided strips, respectively, and the grid structure exhibited superior anti-deformation capabilities compared to the strip structure. The average discrepancy between the calculated values of the established model and the theoretical values was merely 2.38% (maximum error < 5%). Overall, this research offers technical assistance for ensuring the safety of subgrade design and promoting environmental sustainability in engineering, enabling the effective utilization of waste tire grids in sustainable reinforcement applications. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
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13 pages, 751 KiB  
Article
Feline Testicular Biometry and Gonadosomatic Index: Associations Among Conventional Measurements, Mathematical Estimates, and Seminal Parameters
by Mónica Madrigal-Valverde, Rodrigo F. Bittencourt, Antonio Lisboa Ribeiro Filho, Thereza Cristina Calmon de Bittencourt, Isabella de Matos Brandão Carneiro, Luiz Di Paolo Maggitti, Gabriel Felipe Oliveira de Menezes, Carmo Emanuel de Almeida Biscarde, Gleice Mendes Xavier, Paola Pereira das Neves Snoeck and Larissa Pires Barbosa
Animals 2025, 15(15), 2191; https://doi.org/10.3390/ani15152191 - 25 Jul 2025
Viewed by 233
Abstract
The development of biometric techniques in domestic animals has greatly advanced scientific practices in wildlife research. The association between seminal characteristics and body and testicular biometry enables the selection of suitable breeders, though appropriate measurement techniques are required. The present study assessed differences [...] Read more.
The development of biometric techniques in domestic animals has greatly advanced scientific practices in wildlife research. The association between seminal characteristics and body and testicular biometry enables the selection of suitable breeders, though appropriate measurement techniques are required. The present study assessed differences among conventional methods and formulas for estimating testicular parameters. Testicular length, width, and thickness were measured using three methods in 13 adult male domestic cats. Testicular area, volume, and weight were estimated, from which the gonadosomatic index (GSI) was calculated. Sperm were collected using an alpha-2 adrenergic agonist and urethral catheterization, and characterized in terms of volume, vigor, total motility, progressive motility, concentration, plasma membrane integrity, and morphology. The three methods were consistent in terms of testicular area, volume, weight, and GSI. Moderate positive correlations were observed for testicular weight (r = 0.61, p < 0.05) and GSI (r = 0.58, p < 0.05). Testicular parameters showed strong positive correlations among each other (r > 0.80, p < 0.05). We observed a moderate positive correlation between head length and progressive motility (r = 0.65, p < 0.05). In conclusion, all testicular measurement and estimation techniques showed comparable performance. Therefore, testicular biometry is useful for selecting breeding males in feline conservation programs, wherein larger body biometrics are related to improved seminal and reproductive parameters. Full article
(This article belongs to the Section Animal Physiology)
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17 pages, 2089 KiB  
Article
Analytical Periodic Solutions for Non-Homogenous Integrable Dispersionless Equations Using a Modified Harmonic Balance Method
by Muhammad Irfan Khan, Yiu-Yin Lee and Muhammad Danish Zia
Mathematics 2025, 13(15), 2386; https://doi.org/10.3390/math13152386 - 24 Jul 2025
Viewed by 251
Abstract
In this study, we outline a modified harmonic balance method for solving non-homogenous integrable dispersionless equations and obtaining the corresponding periodic solutions, a research field which shows limited investigation. This study is the first to solve this nonlinear problem, based on a recently [...] Read more.
In this study, we outline a modified harmonic balance method for solving non-homogenous integrable dispersionless equations and obtaining the corresponding periodic solutions, a research field which shows limited investigation. This study is the first to solve this nonlinear problem, based on a recently developed harmonic balance method combined with Vieta’s substitution technique. A set of analytical formulas are generated from the modified harmonic balance method and used to compute the approximate periodic solutions of the dispersionless equations. The main advantage of this method is that the computation effort required in the solution procedure can be smaller. The results of the modified harmonic balance method show reasonable agreement with those obtained using the classic harmonic balance method. Our proposed solution method can decouple the nonlinear algebraic equations generated in the harmonic balance process. We also investigated the effects of various parameters on nonlinear periodic responses and harmonic convergence. Full article
(This article belongs to the Special Issue Modeling and Control in Vibrational and Structural Dynamics)
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9 pages, 238 KiB  
Article
An Approximation Formula of the Integral Transform on Wiener Space
by Hyun Soo Chung
Axioms 2025, 14(8), 570; https://doi.org/10.3390/axioms14080570 - 24 Jul 2025
Viewed by 161
Abstract
In this paper, we introduce an integral transform with a kernel defined on the Wiener space. We first establish the existence of the integral transform and present several illustrative examples. As the main result, we derive an approximation theorem for the integral transform. [...] Read more.
In this paper, we introduce an integral transform with a kernel defined on the Wiener space. We first establish the existence of the integral transform and present several illustrative examples. As the main result, we derive an approximation theorem for the integral transform. Our approach demonstrates that the integral transform can be effectively computed even in cases where direct calculation is difficult or infeasible. Full article
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)
22 pages, 11876 KiB  
Article
Revealing Ecosystem Carbon Sequestration Service Flows Through the Meta-Coupling Framework: Evidence from Henan Province and the Surrounding Regions in China
by Wenfeng Ji, Siyuan Liu, Yi Yang, Mengxue Liu, Hejie Wei and Ling Li
Land 2025, 14(8), 1522; https://doi.org/10.3390/land14081522 - 24 Jul 2025
Viewed by 225
Abstract
Research on ecosystem carbon sequestration services and ecological compensation is crucial for advancing carbon neutrality. As a public good, ecosystem carbon sequestration services inherently lead to externalities. Therefore, it is essential to consider externalities in the flow of sequestration services. However, few studies [...] Read more.
Research on ecosystem carbon sequestration services and ecological compensation is crucial for advancing carbon neutrality. As a public good, ecosystem carbon sequestration services inherently lead to externalities. Therefore, it is essential to consider externalities in the flow of sequestration services. However, few studies have examined intra- and inter-regional ecosystem carbon sequestration flows, making regional ecosystem carbon sequestration flows less comprehensive. Against this background, the research objectives of this paper are as follows. The flow of carbon sequestration services between Henan Province and out-of-province regions is studied. In addition, this study clarifies the beneficiary and supply areas of carbon sink services in Henan Province and the neighboring regions at the prefecture-level city scale to obtain a more systematic, comprehensive, and actual flow of carbon sequestration services for scientific and effective eco-compensation and to promote regional synergistic emission reductions. The research methodologies used in this paper are as follows. First, this study adopts a meta-coupling framework, designating Henan Province as the focal system, the Central Urban Agglomeration as the adjacent system, and eight surrounding provinces as remote systems. Regional carbon sequestration was assessed using net primary productivity (NEP), while carbon emissions were evaluated based on per capita carbon emissions and population density. A carbon balance analysis integrated carbon sequestration and emissions. Hotspot analysis identified areas of carbon sequestration service supply and associated benefits. Ecological radiation force formulas were used to quantify service flows, and compensation values were estimated considering the government’s payment capacity and willingness. A three-dimensional evaluation system—incorporating technology, talent, and fiscal capacity—was developed to propose a diversified ecological compensation scheme by comparing supply and beneficiary areas. By modeling the ecosystem carbon sequestration service flow, the main results of this paper are as follows: (1) Within Henan Province, Luoyang and Nanyang provided 521,300 tons and 515,600 tons of carbon sinks to eight cities (e.g., Jiaozuo, Zhengzhou, and Kaifeng), warranting an ecological compensation of CNY 262.817 million and CNY 263.259 million, respectively. (2) Henan exported 3.0739 million tons of carbon sinks to external provinces, corresponding to a compensation value of CNY 1756.079 million. Conversely, regions such as Changzhi, Xiangyang, and Jinzhong contributed 657,200 tons of carbon sinks to Henan, requiring a compensation of CNY 189.921 million. (3) Henan thus achieved a net ecological compensation of CNY 1566.158 million through carbon sink flows. (4) In addition to monetary compensation, beneficiary areas may also contribute through technology transfer, financial investment, and talent support. The findings support the following conclusions: (1) it is necessary to consider the externalities of ecosystem services, and (2) the meta-coupling framework enables a comprehensive assessment of carbon sequestration service flows, providing actionable insights for improving ecosystem governance in Henan Province and comparable regions. Full article
(This article belongs to the Special Issue Land Resource Assessment (Second Edition))
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21 pages, 915 KiB  
Article
A High-Order Proper Orthogonal Decomposition Dimensionality Reduction Compact Finite-Difference Method for Diffusion Problems
by Wenqian Zhang and Hong Li
Math. Comput. Appl. 2025, 30(4), 77; https://doi.org/10.3390/mca30040077 - 23 Jul 2025
Viewed by 116
Abstract
An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation [...] Read more.
An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation approximation. The quartic spline function and (2,2) Padé approximation were utilized in space and time discretization, respectively. The stability and convergence were proven. Moreover, the dimensionality reduction formulas were derived using the proper orthogonal decomposition (POD) method, which is based on the matrix representation of the compact finite-difference scheme. The bases of the POD method were established by cumulative contribution rate of the eigenvalues of snapshot matrix that is different from the traditional ways in which the bases were established by the first eigenvalues. The method of cumulative contribution rate can optimize the degree of freedom. The error analysis of the reduced bases high-order POD finite-difference scheme was provided. Numerical experiments are conducted to validate the soundness and dependability of the reduced-order algorithm. The comparisons between the (2,2) finite-difference method, the traditional POD method, and reduced dimensional method with cumulative contribution rate were discussed. Full article
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15 pages, 1757 KiB  
Article
Development of a Design Formula for Estimating the Residual Strength of Corroded Stiffened Cylindrical Structures
by Sang-Hyun Park, Byoungjae Park, Sang-Rai Cho, Sung-Ju Park and Kookhyun Kim
J. Mar. Sci. Eng. 2025, 13(7), 1381; https://doi.org/10.3390/jmse13071381 - 21 Jul 2025
Viewed by 286
Abstract
This paper develops a novel design formula to estimate the residual strength of corroded stiffened cylindrical structures. It extends a previously established ultimate strength formulation for intact cylinders by introducing a corrosion-induced strength reduction factor. The foundational formula considers failure mode interactions like [...] Read more.
This paper develops a novel design formula to estimate the residual strength of corroded stiffened cylindrical structures. It extends a previously established ultimate strength formulation for intact cylinders by introducing a corrosion-induced strength reduction factor. The foundational formula considers failure mode interactions like yielding, local buckling, overall buckling, and stiffener tripping. This research utilizes recent experimental and numerical investigations on corroded ring-stiffened cylinder models. Experimental results validate the numerical analysis method, showing good agreement in collapse pressures (2–4% difference) and shapes. The validated numerical method is then subject to an extensive parametric study, systematically varying corrosion characteristics. Results indicate a clear relationship between corrosion volume and strength reduction, with overall buckling being more sensitive. Based on these comprehensive results, a new empirical strength reduction factor (ρc) is derived as a function of the corrosion volume ratio (Vnon). This factor is integrated into the existing ultimate strength formula, allowing direct residual strength estimation for corroded structures. The proposed formula is rigorously verified against experimental and numerical data, showing excellent agreement (mean 1.00, COV 5.86%). This research provides a practical, accurate design tool for assessing the integrity and service life of corroded stiffened cylindrical structures. Full article
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