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Keywords = spatial inequalities

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29 pages, 3816 KB  
Article
Inequality, Social Capital, and Crime: A Municipal-Level Mediation Analysis in Mexico
by Luis Lauro Carrillo-Sagástegui and Francisco García-Fernández
Soc. Sci. 2026, 15(9), 570; https://doi.org/10.3390/socsci15090570 (registering DOI) - 24 Aug 2026
Abstract
This study analyzes the relationship between economic inequality, social capital, and crime across Mexican municipalities in 2020, adopting a mediation approach and an exploratory territorial analysis. Using data from the National Council for the Evaluation of Social Development Policy (CONEVAL), the National Institute [...] Read more.
This study analyzes the relationship between economic inequality, social capital, and crime across Mexican municipalities in 2020, adopting a mediation approach and an exploratory territorial analysis. Using data from the National Council for the Evaluation of Social Development Policy (CONEVAL), the National Institute of Statistics and Geography (INEGI), the Executive Secretariat of the National Public Security System (SESNSP), the National Statistical Directory of Economic Units (DENUE), and the National Electoral Institute (INE), a structural social capital index was constructed through Principal Component Analysis (PCA), a structural social capital index was constructed through Principal Component Analysis (PCA), incorporating indicators of civic participation, associational density, and local social infrastructure. The empirical strategy combines ordinary least squares (OLS) regression models, Exploratory Spatial Data Analysis (ESDA), bootstrap mediation models with 5000 resamples, and spatial regression robustness checks. The results show that inequality is positively and significantly associated with municipal crime rates; the Gini index is associated with vehicle theft (β = 0.115, p < 0.001) and homicide (β = 0.073, p < 0.001). After structural covariates are included, inequality loses statistical significance for property crime but remains associated with homicide (β = 0.098, p < 0.001). Social capital shows a significant negative association with both crime outcomes. The mediation analysis indicates a statistically significant indirect pathway linking inequality and crime through structural social capital; however, the form of mediation differs by crime type. For homicide, the evidence is consistent with complementary or partial mediation, whereas the covariate-adjusted vehicle theft model shows a competitive mediation or suppression pattern. The spatial analysis reveals territorial autocorrelation in all variables. Spatial regression robustness checks further show that structural social capital remains negatively associated with both crime outcomes after accounting for spatial dependence. The findings suggest that the inequality–crime relationship depends on contextual factors and local social structures and should be interpreted as statistical associations rather than causal effects. Full article
(This article belongs to the Section Social Stratification and Inequality)
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32 pages, 2115 KB  
Article
Urban Fragmentation and Spatial Inequalities in Public Transport Accessibility: Evidence from El Bayadh, an Intermediate Arid City in Algeria
by Fatima Zohra Mokeddem, Naima Hadj Mohamed, Zahia Meghnous Dris, Zouaoui R. Harrat, Walid Mansour, Mohammed Chatbi, Aida Achour and Nahla Hilal
Urban Sci. 2026, 10(8), 487; https://doi.org/10.3390/urbansci10080487 - 21 Aug 2026
Viewed by 59
Abstract
Rapid urban expansion in arid intermediate cities often produces fragmented urban structures that exacerbate inequalities in public transport accessibility and hinder sustainable mobility. However, the relationships between urban fragmentation, transport accessibility, and travel behavior remain insufficiently explored in pre-Saharan cities. This study investigates [...] Read more.
Rapid urban expansion in arid intermediate cities often produces fragmented urban structures that exacerbate inequalities in public transport accessibility and hinder sustainable mobility. However, the relationships between urban fragmentation, transport accessibility, and travel behavior remain insufficiently explored in pre-Saharan cities. This study investigates these interactions through the case of El Bayadh, Algeria, using an integrated methodology combining urban morphological analysis, Geographic Information Systems (GIS), a household survey of 577 households, traffic counts, institutional interviews, and spatial equality assessment based on the Gini coefficient. Public transport accessibility was evaluated using a 300 m walking threshold, complemented by sensitivity analyses at 400 m and 500 m. The results indicate that approximately 65% of the population lives within 300 m of a bus stop, although coverage is strongly concentrated in central districts. A Gini coefficient of 0.41, provided by the El Bayadh Directorate of Transport and computed across 20 urban zones, indicates moderate-to-high spatial inequalities in accessibility that persist despite increasing the service threshold, suggesting that these disparities are more closely associated with urban fragmentation than with the specific walking-distance threshold used to define service coverage. The transport network comprises 11 bus routes, approximately 160 bus stops, and 90 km of routes; however, limited service quality and uneven spatial distribution contribute to a high dependence on private transport, with 45% of trips made by private car, 35% by taxi, and only 20% by bus. These findings are consistent with accessibility inequalities arising from the mismatch between fragmented urban morphology, centralized urban functions, and the configuration of the public transport network. The proposed framework provides transferable insights for planning more equitable and sustainable mobility systems in rapidly urbanizing arid intermediate cities. Full article
(This article belongs to the Section Urban Mobility and Transportation)
29 pages, 3555 KB  
Article
Spatial Patterns and Driving Factors of Low-Altitude Tourism Bases in China: Implications for Sustainable Regional Planning
by Jiacheng Hu, Lulu Zhang, Yinuo Jia and Yuhao Feng
Sustainability 2026, 18(16), 8598; https://doi.org/10.3390/su18168598 - 21 Aug 2026
Viewed by 144
Abstract
The rapid development of the low-altitude economy is reshaping tourism activities, infrastructure provision, and landscape resource use, yet national-scale research on low-altitude tourism bases remains limited. Using data on 1247 bases in China, this study applies average nearest-neighbor analysis, kernel density estimation, and [...] Read more.
The rapid development of the low-altitude economy is reshaping tourism activities, infrastructure provision, and landscape resource use, yet national-scale research on low-altitude tourism bases remains limited. Using data on 1247 bases in China, this study applies average nearest-neighbor analysis, kernel density estimation, and spatial inequality measures to characterize multi-scale patterns. The study further employs an optimal parameters-based geographical detector within a geographical nature framework to identify influencing factors and interactions. The results reveal significant clustering and regional inequality, with a pronounced east–west divide along the Heihe–Tengchong Line. A diamond-shaped core bounded by Beijing, Hangzhou, Chengdu, and Sanya, together with its 200 km buffer zone, contains 89.17% of all bases. Domestic tourism revenue, the number of low-altitude industry enterprises, general aviation airports, national tourist resorts, and domestic tourist arrivals constitute the leading factors, although the dominant factor combinations vary across base types. Factor interactions are dominated by two-factor and nonlinear enhancement. The three natures form a coupled pathway: first nature provides environmental suitability, second nature transforms resource potential into marketable tourism products, and third nature regulates implementation. General aviation infrastructure acts as an operational interface linking environmental conditions, tourism demand, industrial support, and policy arrangements. The findings provide a basis for differentiated regional zoning and type-specific facility planning, thereby informing the sustainable development of low-altitude tourism. Full article
(This article belongs to the Special Issue Sustainable Development of Regional Tourism)
14 pages, 271 KB  
Article
Phragmén–Lindelöf Alternative Results for the Thermoelasticity of Type III on an Exterior Region in ℝ3
by Jincheng Shi
Symmetry 2026, 18(8), 1406; https://doi.org/10.3390/sym18081406 - 21 Aug 2026
Viewed by 157
Abstract
This paper investigates the spatial asymptotic behaviour of solutions to a coupled thermoelastic system of Green–Naghdi Type III in an exterior domain of R3. The system couples elastodynamics with a second-order heat conduction law and contains indefinite cross-coupling terms between mechanical [...] Read more.
This paper investigates the spatial asymptotic behaviour of solutions to a coupled thermoelastic system of Green–Naghdi Type III in an exterior domain of R3. The system couples elastodynamics with a second-order heat conduction law and contains indefinite cross-coupling terms between mechanical and thermal variables. By constructing a weighted energy functional and deriving a first-order differential inequality in the radial direction, we establish a Phragmén–Lindelöf alternative: for each fixed time, the total energy either grows exponentially or decays exponentially as r, with an explicit decay rate that depends on the material coefficients and a free parameter ω. This dichotomy itself reveals a fundamental symmetry in the spatial behaviour—growth versus decay—which is intimately linked to the radial symmetry of the exterior geometry and the inherent structure of the coupled system. The result provides a complete characterization of spatial stability for this thermoelastic model in unbounded exterior domains. Full article
(This article belongs to the Section B: Mathematics)
23 pages, 1684 KB  
Review
The Erosion of Work–Life Boundaries and Burnout: A Narrative Review of Mechanisms, Vulnerable Populations and Public Health Implications
by Julien Lochmann, Klaus Patzke, Stefan Wahl, Fabian Renger and Attila Czirfusz
Psychiatry Int. 2026, 7(4), 186; https://doi.org/10.3390/psychiatryint7040186 - 21 Aug 2026
Viewed by 176
Abstract
The digital transformation of work has increasingly blurred the temporal, spatial, and psychological boundaries between professional and personal life. As a result, structural conditions have emerged that are associated with an elevated risk of burnout. This narrative review draws on literature identified through [...] Read more.
The digital transformation of work has increasingly blurred the temporal, spatial, and psychological boundaries between professional and personal life. As a result, structural conditions have emerged that are associated with an elevated risk of burnout. This narrative review draws on literature identified through searches of Web of Science, Scopus and PubMed covering publications from 2004 to early 2026, which yielded 36 included studies, supplemented by further sources identified outside that search. It integrates key theoretical perspectives, including boundary theory, the Areas of Worklife model, the Job Demands-Resources framework and Conservation of Resources theory. Across diverse occupational contexts, three pathways recur: rising work-family conflict, reduced ability to psychologically detach from work during non-work time and the gradual depletion of personal resources. Structural drivers, comprising organisational availability norms, leadership behaviour, technology and platform design, workload, and economic precarity, are treated as the conditions under which exposure arises, and the review argues that responses pitched at individual coping are correspondingly limited. The public health implications extend beyond mental health, encompassing cardiovascular risk associated with long working hours, strain on healthcare systems, productivity losses and widening health inequities along gendered and socioeconomic lines. Addressing these challenges requires multilevel interventions, including organisational job redesign, leadership development, enforceable right-to-disconnect policies and greater recognition of recovery as a public health priority. At the same time, there remains a need for more longitudinal and intervention-based research, particularly in non-Western contexts. Full article
(This article belongs to the Section Mental Health)
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36 pages, 15957 KB  
Article
Who Belongs in the Neighbourhood? Food Delivery Riders’ Spatial Experience and Perceived Inclusion in Chinese Gated Communities
by Yi Li, Li Zhu, Haoyu Deng, Quhan Chen, Siyu Zhang, Xiangxiang Chen and Chenxi Song
Buildings 2026, 16(16), 3314; https://doi.org/10.3390/buildings16163314 - 20 Aug 2026
Viewed by 197
Abstract
As China’s dominant urban housing form, gated residential communities deploy layered spatial access controls governing who may enter and move through neighbourhood space. While neighbourhood social sustainability has attracted substantial scholarly attention, how micro-spatial governance arrangements affect the inclusiveness of residential built environments [...] Read more.
As China’s dominant urban housing form, gated residential communities deploy layered spatial access controls governing who may enter and move through neighbourhood space. While neighbourhood social sustainability has attracted substantial scholarly attention, how micro-spatial governance arrangements affect the inclusiveness of residential built environments toward essential service workers remains underexplored. Drawing on Lefebvre’s theory of the production of space, this study uses food delivery riders—who navigate gated community access controls dozens of times daily—as an analytical lens to evaluate how neighbourhood spatial governance shapes social inclusiveness. Vignette-based survey data from 445 riders across 157 cities in 27 Chinese provinces were analysed using structural equation modeling. Results show that cumulative anxiety from procedural delays, detours, and elevator waiting is the dominant pathway through which spatial governance undermines riders’ perceived spatial inclusion—operationalised through occupational dignity indicators—with elevator-based spatial stratification identified as a concrete, low-cost intervention target within the spatial-channeling mechanism. Technology-mediated access partially mitigates face-to-face exclusion but leaves underlying spatial inequalities intact. Demographic invariance across all tested variables confirms that diminished inclusion arises from the governance regime itself. The findings position neighbourhood spatial governance as a measurable dimension of urban social sustainability—one concretely testable through the experience of essential service workers—and identify low-cost built-environment interventions for inclusive residential design. While the study focuses on riders as a single user group, the analytical framework is transferable to evaluating how residential built environments accommodate diverse non-resident populations. Full article
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20 pages, 6356 KB  
Article
Pandemic-Associated Shifts and Spatial Inequality in Public Attention to Pulmonary Function Testing in China: A 14-Year Baidu Index Study
by Cai Chen, Dedong Ma and Tao Jing
Healthcare 2026, 14(16), 2640; https://doi.org/10.3390/healthcare14162640 - 20 Aug 2026
Viewed by 155
Abstract
Background/Objectives: Pulmonary function tests (PFTs), especially spirometry, are important for chronic respiratory disease diagnosis and management, but Baidu-based online search interest in PFT-related information remains insufficiently characterized. This study examined long-term Baidu search activity for a selected PFT-related keyword in China from 2011 [...] Read more.
Background/Objectives: Pulmonary function tests (PFTs), especially spirometry, are important for chronic respiratory disease diagnosis and management, but Baidu-based online search interest in PFT-related information remains insufficiently characterized. This study examined long-term Baidu search activity for a selected PFT-related keyword in China from 2011 to 2024, with attention to pandemic-period changes, provincial variation, spatial inequality, and associated socioeconomic factors. Methods: We analyzed Baidu Index data from 1 January 2011 to 31 December 2024. The selected PFT-related keyword, “pulmonary function instrument,” was compared with “blood pressure monitor” and “blood glucose meter.” Daily Baidu Index values were aggregated into monthly and annual series. Temporal trends, relative search-intensity ratios, interrupted time-series analysis, inequality indices, fixed-effects regression, subgroup heterogeneity, and convergence dynamics were assessed. Results: PFT-related Baidu search activity remained lower than that for blood pressure and glucose monitoring, with relative search-intensity ratios below 0.35. Descriptively, PFT-related searches increased during 2020–2022; however, the re-specified seasonality-adjusted ITSA using unsmoothed monthly observations did not provide strong statistical evidence for an immediate level change at pandemic onset or a sustained slope change. Provincial differences persisted, with higher values generally observed in several eastern coastal provinces. Inequality indices were lower on average during 2020–2022 but fluctuated over time, and beta-convergence analyses provided limited statistical evidence of systematic catch-up among initially low-index provinces. Urbanization, per capita GDP, and population aging were positively associated with PFT-related Baidu Index values, while subgroup findings were interpreted as exploratory ecological associations. Conclusions: PFT-related Baidu search activity in China remained lower than search activity for blood pressure and glucose monitoring and showed persistent provincial variation. These findings suggest lower visibility of PFT-related information within the Baidu-based online environment. Full article
(This article belongs to the Topic Advances in Chronic Disease Management)
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36 pages, 1594 KB  
Article
Sustainable Land Transport Infrastructure System Composition and Urban–Rural Income Inequality: Evidence from Chinese Prefecture-Level Cities
by Yaojun Qi, Fauzan Mohd Jakarni, Nur Ainina Mustafa and Nur ’Atirah Muhadi
Sustainability 2026, 18(16), 8509; https://doi.org/10.3390/su18168509 - 19 Aug 2026
Viewed by 127
Abstract
Land transport infrastructure (LTI) is a core component of sustainable transport systems, shaping mobility, efficiency, and the spatial distribution of development gains. Existing studies of urban–rural income inequality mainly focus on individual transport modes or aggregate infrastructure scale, with limited attention to transport-system [...] Read more.
Land transport infrastructure (LTI) is a core component of sustainable transport systems, shaping mobility, efficiency, and the spatial distribution of development gains. Existing studies of urban–rural income inequality mainly focus on individual transport modes or aggregate infrastructure scale, with limited attention to transport-system composition and its contextual dependence. This study addresses this gap by conceptualizing LTI as a layered system and examining how its internal composition is associated with urban–rural income inequality across different levels of urbanization and economic development. Using a balanced panel of 286 prefecture-level cities from 2013 to 2023, the study constructs ratio-based indicators of compositional shifts within road systems, within rail systems, and between rail and road infrastructure. Two-way fixed-effects models incorporate interactions with urbanization and economic development. Conditional marginal-effect maps are then used to identify how these associations change across development contexts. The results reveal a clear stage-dependent pattern. Urbanization generally attenuates the inequality-widening association of mobility-oriented upgrading, whereas economic development influences whether such upgrading reinforces spatial polarization or supports wider diffusion. When urbanization and development are both sufficiently advanced, the marginal association may shift toward inequality reduction. At earlier stages, accessibility-oriented roads and conventional rail tend to show stronger equalizing associations. Mobility-oriented roads and high-speed rail are more likely to be associated with narrower inequality in more advanced settings. Mechanism-oriented analyses yield evidence consistent with two potential channels: the agricultural–non-agricultural labor-productivity gap and the non-agricultural employment share. The extended analyses and robustness checks broadly support the main findings. These findings indicate that transport infrastructure upgrading should be evaluated not only in terms of efficiency, but also according to whether the resulting infrastructure mix broadens access to opportunities, improves resource allocation, and supports inclusive regional development. Full article
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31 pages, 38899 KB  
Article
Spatial Inequality and Infrastructure-Based Carbon Lock-In in Green Logistics: Evidence from China
by Hao Zhang, Zhonghua Xu, Peng Wang and Jie He
Sustainability 2026, 18(16), 8502; https://doi.org/10.3390/su18168502 - 19 Aug 2026
Viewed by 116
Abstract
The logistics industry remains a critical bottleneck for decarbonization due to its extensive physical networks and high-carbon path dependencies. To address the spatial heterogeneity and transition constraints in the logistics industry of China, this study proposes a Performance–Topology–Mechanism (PTM) framework. Analyzing panel data [...] Read more.
The logistics industry remains a critical bottleneck for decarbonization due to its extensive physical networks and high-carbon path dependencies. To address the spatial heterogeneity and transition constraints in the logistics industry of China, this study proposes a Performance–Topology–Mechanism (PTM) framework. Analyzing panel data from 30 Chinese provinces, we integrate a Super-SBM model with the Global Malmquist–Luenberger (GML) index, Dagum Gini decomposition, and a panel Tobit model to decode the spatiotemporal dynamics of green innovation performance (GIP) and its underlying spatial lock-in mechanisms. The results reveal a steady but spatially uneven increase in the national GIP (from 0.4526 to 0.5724), characterized by a leading East and a lagging West/Northeast. GML decomposition indicates this growth is predominantly driven by outward shifts in the technological frontier rather than efficiency improvements, highlighting the weak spatial conversion of green technologies into transport optimization. Topological tracing demonstrates that inter-regional disparities have become the dominant source of spatial inequality, with their contribution rising from 60% to 75%. Spatial autocorrelation further exposes a deepening core–periphery polarization and persistent low-performance spatial lock-in. Crucially, the mechanism analysis identifies a pronounced infrastructure-based carbon lock-in. While economic capacity and green patents stimulate GIP, road network density exerts a significant negative effect, reflecting a systemic path dependence on high-carbon road freight. The findings suggest that decarbonizing transport logistics requires shifting from singular technological investments toward multimodal transport restructuring, overcoming physical network dependencies, and promoting the regional diffusion of green innovations. These findings provide an empirical basis for differentiated green-logistics policies, coordinated low-carbon transport infrastructure planning, and cross-regional diffusion of green technologies. Full article
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25 pages, 2898 KB  
Article
Siting Versus Capitalization of Disamenity and Amenity Facilities in Housing and Land Prices Using Integrated Multi-Source Spatial Data in South Korea
by Solhee Kim and Yunhee Park
Land 2026, 15(8), 1500; https://doi.org/10.3390/land15081500 - 18 Aug 2026
Viewed by 194
Abstract
Disamenity and amenity facilities pull property values in opposite directions, yet prior studies have treated disamenities as a homogeneous category and have been constrained by data scattered across agencies and by mismatched spatial scales. This study integrates multi-source spatial data, comprising 3426 sub-districts [...] Read more.
Disamenity and amenity facilities pull property values in opposite directions, yet prior studies have treated disamenities as a homogeneous category and have been constrained by data scattered across agencies and by mismatched spatial scales. This study integrates multi-source spatial data, comprising 3426 sub-districts (eup-myeon-dong) nationwide, a 500 m population grid of 376,668 cells, and the actual point locations of individual facilities, into a single spatial framework and applies a multi-method design that combines a spatial Durbin model (SDM), explainable machine learning (XGBoost–SHAP), an environmental-justice analysis, and a micro-siting analysis. Four findings emerge. First, not all disamenities are associated with lower prices: only pollution-emitting facilities with a clear emission signature, namely, sewage treatment plants and incinerators, capitalize robustly as cross-sectional associations, into both housing prices and officially assessed land values, with the effect extending into neighboring sub-districts rather than staying purely local. The other disamenities show no robust total effect on either price; their estimates are small or unstable across specifications. Second, capitalization of pollution-emitting facilities is pronounced in the urban sample and disappears in the rural one, and the coefficient structure differs overall between urban and rural areas (global Chow test, p < 10−21). Third, micro-siting analysis shows that where a facility is placed (siting) and what it leaves behind in prices (capitalization) are distinct layers, and that capitalization tracks the population a facility keeps nearby rather than its nuisance type: pollution-emitting facilities retain enough nearby housing for their burden to register, whereas funerary facilities sited far from people do not. Fourth, the environmental inequity of pollution exposure runs along income rather than age and concentrates in cities rather than in rural areas: the exposure rate among residents of low-income urban sub-districts (49%) is 2.5 times that of the urban population as a whole (19%), while the greater Seoul metropolitan area remains comparatively insulated. These layered findings were possible only once the dispersed spatial data had been integrated and standardized, and the study demonstrates that fusing and efficiently managing spatial data is a precondition for evidence-based land-use and environmental policy. Full article
(This article belongs to the Section Land Socio-Economic and Political Issues)
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24 pages, 6747 KB  
Article
People–Land Coordination Under Uneven Development: Mismatch Patterns, Spatiotemporal Evolution, and Driving Factors in China’s Urban Agglomerations
by Weimin Wang and Hyukku Lee
Sustainability 2026, 18(16), 8454; https://doi.org/10.3390/su18168454 - 18 Aug 2026
Viewed by 152
Abstract
Urban agglomerations concentrate human populations, economic activities, and land development, but gains in land-use efficiency do not necessarily progress synchronously with improvements in human-development capability. This study examines the coordination and mismatch between population high-quality development (PHQD)—referring specifically to the high-quality development of [...] Read more.
Urban agglomerations concentrate human populations, economic activities, and land development, but gains in land-use efficiency do not necessarily progress synchronously with improvements in human-development capability. This study examines the coordination and mismatch between population high-quality development (PHQD)—referring specifically to the high-quality development of the human population—and land green use efficiency (LGUE) across 131 cities in six major Chinese urban agglomerations from 2011 to 2023. PHQD is measured using the entropy-weighted TOPSIS method. LGUE is measured using a non-oriented global super-efficiency slacks-based measure (SBM) model with undesirable outputs. People–land coordination is assessed using a modified coupling coordination degree (MCCD) model combined with a relative development index (RDI). Kernel density estimation, Dagum Gini decomposition, and Geodetector are applied to analyze distribution dynamics, disparities, and spatially stratified associations. MCCD rose from 0.311 to 0.419, although most cities remained at relatively low coordination levels. PHQD-lagging was the dominant mismatch type in 2023, involving 98 of 131 cities. Overall MCCD inequality declined from 0.138 to 0.103, while transvariation replaced between-group differences as the largest disparity component. Economic development had the strongest explanatory power, and all pairwise interaction q values exceeded the corresponding single-factor q values. Sustainable urban transformation therefore requires coordinated investment in human capital and public services alongside continued improvements in resource- and environmentally constrained land-use efficiency. Full article
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16 pages, 334 KB  
Article
Unconditional Optimal Error Estimates of a Linearized Nonuniform Alikhanov Scheme for Nonlinear Superdiffusion Equations
by Mingze Sun and Chaobao Huang
Mathematics 2026, 14(16), 2972; https://doi.org/10.3390/math14162972 - 17 Aug 2026
Viewed by 229
Abstract
In this paper, we consider a nonlinear fractional superdiffusion equation involving a Caputo derivative of order α(1,2). Solutions to this class of problems typically exhibit weak singularities near the initial time. To handle this singularity, we [...] Read more.
In this paper, we consider a nonlinear fractional superdiffusion equation involving a Caputo derivative of order α(1,2). Solutions to this class of problems typically exhibit weak singularities near the initial time. To handle this singularity, we introduce an auxiliary variable p:=Dtα/2(utu1) and reformulate the original problem as an equivalent coupled system. This system is then discretized using the nonuniform Alikhanov scheme in time, the conforming Galerkin finite element method in space, and Newton linearization for the nonlinear term. We prove that the numerical solutions remain uniformly bounded, independent of the temporal and spatial mesh parameters. Combining this result with a discrete fractional Grönwall inequality and a temporal-spatial splitting argument, we establish unconditional optimal error estimates of order O(Nmin{2,rα/2}+hk). Finally, numerical experiments are presented to verify the sharpness of the theoretical convergence rates. Full article
(This article belongs to the Section E: Applied Mathematics)
20 pages, 3282 KB  
Article
The Pandemic’s Shock to the Mining Industry: A Counterfactual Analysis of Global Water–Carbon–Economy Linkages
by Zhen Wang, Xudong Yuan, Yulun Xiao, Jiaquan Zhang, Meihua Song, Lianhe Li, Lien-Chieh Lee and Chi-Hsiang Liu
Environments 2026, 13(8), 454; https://doi.org/10.3390/environments13080454 - 17 Aug 2026
Viewed by 295
Abstract
The mining industry is a cornerstone of global energy security and industrial supply chains, yet its resilience to systemic disruptions such as COVID-19 has been critically overlooked. This disruption provided a rare opportunity to trace supply-chain impacts. Using an environmentally extended multi-regional input-output [...] Read more.
The mining industry is a cornerstone of global energy security and industrial supply chains, yet its resilience to systemic disruptions such as COVID-19 has been critically overlooked. This disruption provided a rare opportunity to trace supply-chain impacts. Using an environmentally extended multi-regional input-output (EEMRIO) model integrated with a Criteria Importance Through Intercriteria Correlation (CRITIC) weighted approach. We compare pandemic trajectories with counterfactual no-pandemic trajectories: the no-pandemic model (calibrated on 2004–2018) projects 2019–2025, while the pandemic model (calibrated through 2023) projects 2023–2025, with 2023 serving as the observed baseline and transition year. Our findings reveal a transient reduction in mining water and carbon footprints, juxtaposed with stark economic contractions: mining value fell by 40% in China, 37% in India, and 13% in the United States. The weighted component among the water-carbon-value (WVC) analysis further uncovers a tripolar spatial pattern, categorizing countries into financial hubs with high value, such as Switzerland, carbon-locked exporters like Brunei, and water-stressed regions, including Cambodia. Despite absorbing substantial embodied environmental burdens, China maintained its position as the global value hub. These insights underscore the urgency of policies that enhance structural efficiency, decarbonize the power sector, and foster supply chain diversification to decouple economic value from environmental pressures while mitigating spatial inequalities. Full article
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20 pages, 3624 KB  
Article
Spatial Allocation Imbalance of Urban Road Infrastructure Level in Major Chinese Cities
by Jianjin Chen, Dingli Liu, Yanchang Wang and Yao Huang
Sustainability 2026, 18(16), 8379; https://doi.org/10.3390/su18168379 - 16 Aug 2026
Viewed by 259
Abstract
The spatial allocation of urban road infrastructure directly affects urban operational efficiency, social equity, and ecological environmental quality. Taking 36 major Chinese cities as the research subjects and drawing on data from municipal statistical yearbooks, this study employs a composite index method, Theil [...] Read more.
The spatial allocation of urban road infrastructure directly affects urban operational efficiency, social equity, and ecological environmental quality. Taking 36 major Chinese cities as the research subjects and drawing on data from municipal statistical yearbooks, this study employs a composite index method, Theil index decomposition, and correlation analysis to reveal spatial differentiation patterns, imbalances, and driving factors of urban road infrastructure levels, based on both aggregate and average indicators. The results indicate that the aggregate road infrastructure level exhibits a “high in the southeast, low in the northwest” pattern along the Hu Huanyong Line, while the average road infrastructure level reveals relatively lower performance in some first-tier cities. Imbalances exist in both aggregate and average dimensions, with Theil indices of 0.231 and 0.059, respectively; intra-regional disparities contribute more to total inequality than inter-regional disparities. Urban permanent population (ridge regression coefficient: 0.1991) and fiscal revenue (ridge regression coefficient: −0.1087) are the core driving factors among the four influencing factors of aggregate road infrastructure level spatial differentiation, whereas GDP (−0.0318) and built-up area (0.0703) exert only marginal effects. This suggests that current aggregate urban road infrastructure levels are shaped by the interplay of urbanization stage, economic development level, fiscal system, and spatial planning policies, all operating within the constraints imposed by the city’s natural geographical conditions, and have not yet adequately addressed residents’ demand for spatial equity. The study recommends establishing differentiated investment mechanisms, optimizing road network density in developed cities, and constructing a spatial matching early-warning system to promote people-oriented new urbanization and coordinated regional sustainable development. Full article
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27 pages, 3995 KB  
Article
Mask and Contiguity-Constrained Subarray Design for SAR Antenna Arrays
by Tianxing Zhang, Haoxuan Qiao, Deqing Mao and Ye Yuan
Remote Sens. 2026, 18(16), 2755; https://doi.org/10.3390/rs18162755 - 15 Aug 2026
Viewed by 136
Abstract
In high-resolution wide-swath (HRWS) spaceborne synthetic aperture radar (SAR) systems, clustered phased array (CPA) architectures alleviate hardware costs but face critical subarray synthesis challenges: manually prescribed pattern masks, redundant equality matching, and unrealizable crossover topologies. This paper proposes a mask- and contiguity-constrained power [...] Read more.
In high-resolution wide-swath (HRWS) spaceborne synthetic aperture radar (SAR) systems, clustered phased array (CPA) architectures alleviate hardware costs but face critical subarray synthesis challenges: manually prescribed pattern masks, redundant equality matching, and unrealizable crossover topologies. This paper proposes a mask- and contiguity-constrained power pattern matching method (MC-PMM) to address these limitations. First, a semidefinite programming (SDP) procedure constructs an SAR-metric-aware SDP-relaxed reference mask for the noise equivalent sigma zero (NESZ) and range ambiguity-to-signal ratio (RASR) requirements within the relaxed covariance space. Second, a dynamic programming (DP) strategy is integrated with a novel mask-constrained iterative projection method (Mask-IPM) to optimize physically contiguous partitions and weights. By transforming equality waveform fitting into mask-violation-based inequality matching, MC-PMM focuses restricted spatial degrees of freedom onto critical performance boundaries. Simulations on a 64-element array demonstrate that, at a subarray ratio of 3/4, MC-PMM achieves a 100% crossover-free topology. Furthermore, relative to the conventional equality matching framework, it lowers the mean RASR by 24.50 dB, with a negligible worst-case NESZ degradation of under 0.4 dB. Full article
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