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Keywords = multidimensional variational inequality

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23 pages, 1099 KB  
Article
Assessing the Determinants of Energy Poverty in Jordan Based on a Novel Composite Index
by Mohammad M. Jaber, Ana Stojilovska and Hyerim Yoon
Urban Sci. 2025, 9(7), 263; https://doi.org/10.3390/urbansci9070263 - 8 Jul 2025
Viewed by 1574
Abstract
Energy poverty, resulting from poor energy efficiency and economic and social barriers to accessing appropriate, modern, and sustainable energy services, remains a critical issue in Jordan, a country facing growing climate pressures, particularly given its history of rapid urbanization. This study examines energy [...] Read more.
Energy poverty, resulting from poor energy efficiency and economic and social barriers to accessing appropriate, modern, and sustainable energy services, remains a critical issue in Jordan, a country facing growing climate pressures, particularly given its history of rapid urbanization. This study examines energy poverty through a multidimensional lens, considering its spatial and socio-demographic variations across Jordan. Drawing on data from 19,475 households, we apply a novel energy poverty index and binary logistic regression to analyze key determinants of energy poverty and discuss their intersection with climate vulnerability. The energy poverty index (EPI) is structured around four pillars: housing, fuel, cooling, and wealth. The results show that 51% of households in Jordan are affected by energy poverty. Contributing factors include geographic location, gender, age, education level, dwelling type, ownership of cooling appliances, and financial stability. The results indicate that energy poverty is both a socio-economic and infrastructural issue, with the highest concentrations in the northern and southern regions of the country, areas also vulnerable to climate risks such as drought and extreme heat. Our findings emphasize the need for integrated policy approaches that simultaneously address income inequality, infrastructure deficits, and environmental stressors. Targeted strategies are needed to align social and climate policies for effective energy poverty mitigation and climate resilience planning in Jordan. Full article
(This article belongs to the Special Issue Sustainable Energy Management and Planning in Urban Areas)
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30 pages, 7559 KB  
Article
Deciphering Socio-Spatial Integration Governance of Community Regeneration: A Multi-Dimensional Evaluation Using GBDT and MGWR to Address Non-Linear Dynamics and Spatial Heterogeneity in Life Satisfaction and Spatial Quality
by Hong Ni, Jiana Liu, Haoran Li, Jinliu Chen, Pengcheng Li and Nan Li
Buildings 2025, 15(10), 1740; https://doi.org/10.3390/buildings15101740 - 20 May 2025
Cited by 1 | Viewed by 720
Abstract
Urban regeneration is pivotal to sustainable development, requiring innovative strategies that align social dynamics with spatial configurations. Traditional paradigms increasingly fail to tackle systemic challenges—neighborhood alienation, social fragmentation, and resource inequality—due to their inability to integrate human-centered spatial governance. This study addresses these [...] Read more.
Urban regeneration is pivotal to sustainable development, requiring innovative strategies that align social dynamics with spatial configurations. Traditional paradigms increasingly fail to tackle systemic challenges—neighborhood alienation, social fragmentation, and resource inequality—due to their inability to integrate human-centered spatial governance. This study addresses these shortcomings with a novel multidimensional framework that merges social perception (life satisfaction) analytics with spatial quality (GIS-based) assessment. At its core, we utilize geospatial and machine learning models, deploying an ensemble of Gradient Boosted Decision Trees (GBDT), Random Forest (RF), and multiscale geographically weighted regression (MGWR) to decode nonlinear socio-spatial interactions within Suzhou’s community environmental matrix. Our findings reveal critical intersections where residential density thresholds interact with commercial accessibility patterns and transport network configurations. Notably, we highlight the scale-dependent influence of educational proximity and healthcare distribution on community satisfaction, challenging conventional planning doctrines that rely on static buffer-zone models. Through rigorous spatial econometric modeling, this research uncovers three transformative insights: (1) Urban environment exerts a dominant influence on life satisfaction, accounting for 52.61% of the variance. Air quality emerges as a critical determinant, while factors such as proximity to educational institutions, healthcare facilities, and public landmarks exhibit nonlinear effects across spatial scales. (2) Housing price growth in Suzhou displays significant spatial clustering, with a Moran’s I of 0.130. Green space coverage positively correlates with price appreciation (β = 21.6919 ***), whereas floor area ratio exerts a negative impact (β = −4.1197 ***), highlighting the trade-offs between density and property value. (3) The MGWR model outperforms OLS in explaining housing price dynamics, achieving an R2 of 0.5564 and an AICc of 11,601.1674. This suggests that MGWR captures 55.64% of pre- and post-pandemic price variations while better reflecting spatial heterogeneity. By merging community-expressed sentiment mapping with morphometric urban analysis, this interdisciplinary research pioneers a protocol for socio-spatial integrated urban transitions—one where algorithmic urbanism meets human-scale needs, not technological determinism. These findings recalibrate urban regeneration paradigms, demonstrating that data-driven socio-spatial integration is not a theoretical aspiration but an achievable governance reality. Full article
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26 pages, 10373 KB  
Article
Using Digital Tools to Understand Global Development Continuums
by J. de Curtò and I. de Zarzà
Societies 2025, 15(3), 65; https://doi.org/10.3390/soc15030065 - 7 Mar 2025
Viewed by 697
Abstract
Traditional classifications of global development, such as the developed/developing dichotomy or Global North/South, often oversimplify the intricate landscape of human development. This paper leverages computational tools, advanced visualization techniques, and mathematical modeling to challenge these conventional categories and reveal a continuous development spectrum [...] Read more.
Traditional classifications of global development, such as the developed/developing dichotomy or Global North/South, often oversimplify the intricate landscape of human development. This paper leverages computational tools, advanced visualization techniques, and mathematical modeling to challenge these conventional categories and reveal a continuous development spectrum among nations. By applying hierarchical clustering, multidimensional scaling, and interactive visualizations to Human Development Index (HDI) data, we identify “development neighborhoods”—clusters of countries that exhibit similar development patterns, sometimes across geographical boundaries. Our methodology combines network theory, statistical physics, and digital humanities approaches to model development as a continuous field, introducing novel metrics for development potential and regional inequality. Through analysis of HDI data from 193 countries (1990–2022), we demonstrate significant regional variations in development trajectories, with Africa showing the highest mean change rate (28.36%) despite maintaining the lowest mean HDI (0.557). The implementation of circle packing and radial dendrogram visualizations reveals both population dynamics and development continuums, while our mathematical framework provides rigorous quantification of development distances and cluster stability. This approach not only uncovers sophisticated developmental progressions but also emphasizes the importance of continuous frameworks over categorical divisions. The findings highlight how digital humanities tools can enhance our understanding of global development, providing policymakers with insights that traditional methods might overlook. Our methodology demonstrates the potential of computational social science to offer more granular analyses of development, supporting policies that recognize the diversity within regional and developmental clusters, while our mathematical framework provides a foundation for future quantitative studies in development economics. Full article
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26 pages, 1374 KB  
Review
Ableism and Employment: A Scoping Review of the Literature
by Ramona H. Sharma, Renée Asselin, Timothy Stainton and Rachelle Hole
Soc. Sci. 2025, 14(2), 67; https://doi.org/10.3390/socsci14020067 - 28 Jan 2025
Cited by 1 | Viewed by 4457
Abstract
Background: Ableism obstructs employment equity for disabled individuals. However, research lacks a comprehensive understanding of how ableism multidimensionally manifests across job types, disability types, stages of employment, and intersecting identities. Objectives: This scoping review examines how ableism affects disabled workers and jobseekers, as [...] Read more.
Background: Ableism obstructs employment equity for disabled individuals. However, research lacks a comprehensive understanding of how ableism multidimensionally manifests across job types, disability types, stages of employment, and intersecting identities. Objectives: This scoping review examines how ableism affects disabled workers and jobseekers, as well as its impacts on employment outcomes, variations across disabilities and identities, and the best practices for addressing these. Eligibility Criteria: The included articles were 109 peer-reviewed empirical studies conducted in the US, Canada, Australia, New Zealand, the UK, Ireland, Denmark, Sweden, Iceland, Norway, and Finland between 2018 and 2023. Sources of Evidence: Using terms related to disability, ableism, and employment, the databases searched included Sociology Collection, CINAHL, PsycInfo, Web of Science, SCOPUS, Education Source, Academic Search Complete, and ERIC. Charting Methods: Data were extracted in tabular form and analyzed through thematic narrative synthesis to identify study characteristics, ableist barriers within employment, intersectional factors, and best practices. Results: Ableism negatively impacts employment outcomes through barriers within the work environment, challenges in disclosing disabilities, insufficient accommodations, and workplace discrimination. Intersectional factors intensify inequities, particularly for BIPOC, women, and those with invisible disabilities. Conclusions: Systemic, intersectional strategies are needed to address ableism, improve policies, and foster inclusive workplace practices. Full article
(This article belongs to the Section Work, Employment and the Labor Market)
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25 pages, 722 KB  
Article
Numerical Approximations and Fractional Calculus: Extending Boole’s Rule with Riemann–Liouville Fractional Integral Inequalities
by Abdul Mateen, Wali Haider, Asia Shehzadi, Hüseyin Budak and Bandar Bin-Mohsin
Fractal Fract. 2025, 9(1), 52; https://doi.org/10.3390/fractalfract9010052 - 18 Jan 2025
Viewed by 1268
Abstract
This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable [...] Read more.
This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integrals is established, forming the foundation for deriving novel fractional Boole-type inequalities tailored to differentiable convex functions. The proposed framework encompasses a wide range of functional classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation, thereby broadening the applicability of these inequalities to diverse mathematical settings. The research emphasizes the importance of the Riemann–Liouville fractional operator in solving problems related to non-integer-order differentiation, highlighting its pivotal role in enhancing classical inequalities. These newly established inequalities offer sharper error bounds for various numerical quadrature formulas in classical calculus, marking a significant advancement in computational mathematics. Numerical examples, computational analysis, applications to quadrature formulas and graphical illustrations substantiate the efficacy of the proposed inequalities in improving the accuracy of integral approximations, particularly within the context of fractional calculus. Future directions for this research include extending the framework to incorporate q-calculus, symmetrized q-calculus, alternative fractional operators, multiplicative calculus, and multidimensional spaces. These extensions would enable a comprehensive exploration of Boole’s formula and its associated error bounds, providing deeper insights into its performance across a broader range of mathematical and computational settings. Full article
(This article belongs to the Section General Mathematics, Analysis)
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22 pages, 307 KB  
Article
Multidimensional Inequality Metrics for Sustainable Business Development
by Daniel Felix Ahelegbey and Paolo Giudici
Mathematics 2024, 12(22), 3633; https://doi.org/10.3390/math12223633 - 20 Nov 2024
Cited by 3 | Viewed by 1224
Abstract
This paper introduces a novel methodology for measuring and decomposing multidimensional inequality, allowing for the breakdown of overall inequality into contributions from distinct dimensions. This approach offers valuable insights for sustainable business development by identifying economic sectors where Environmental, Social, or Governance (ESG) [...] Read more.
This paper introduces a novel methodology for measuring and decomposing multidimensional inequality, allowing for the breakdown of overall inequality into contributions from distinct dimensions. This approach offers valuable insights for sustainable business development by identifying economic sectors where Environmental, Social, or Governance (ESG) practices are most unequal and thus may benefit from policy intervention. Additionally, it explores the relationship between company size and sustainability, highlighting that the most concentrated sectors tend to exhibit the greatest ESG inequality. Applying this methodology to a sample of over 1000 small and medium-sized enterprises across various sectors in Italy, our analysis of the multidimensional index for 2022 reveals notable disparities in corporate financial performance and ESG adoption. Specifically, the manufacturing sector exhibited the highest inequality in financial performance, with an index of 0.77, indicating significant variation in financial health and firm size. Conversely, the financial services sector showed lower financial inequality, with an index of 0.23, suggesting more uniform outcomes. On the ESG front, the financial sector demonstrated the highest inequality, particularly in environmental and social dimensions, with an average Gini coefficient of 0.26, while the manufacturing sector displayed a more consistent ESG performance, with an average Gini of 0.19. These findings underscore sector-specific patterns in financial and ESG dimensions, providing a foundation for targeted interventions to reduce disparities. Full article
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14 pages, 268 KB  
Article
Weak Sharp Type Solutions for Some Variational Integral Inequalities
by Savin Treanţă and Tareq Saeed
Axioms 2024, 13(4), 225; https://doi.org/10.3390/axioms13040225 - 28 Mar 2024
Cited by 1 | Viewed by 1138
Abstract
Weak sharp type solutions are analyzed for a variational integral inequality defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well. Also, an illustrative numerical application is provided. [...] Read more.
Weak sharp type solutions are analyzed for a variational integral inequality defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well. Also, an illustrative numerical application is provided. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities)
18 pages, 1015 KB  
Review
A Scoping Review of the Effects of Ambient Air Quality on Cognitive Frailty
by James Robert Hodgson, Charlotte Benkowitz, Brian C. Castellani, Amanda Ellison, Rammina Yassaie, Helen Twohig, Roshni Bhudia, Otto-Emil Ilmari Jutila and Sally Fowler-Davis
Environments 2024, 11(1), 4; https://doi.org/10.3390/environments11010004 - 20 Dec 2023
Cited by 3 | Viewed by 6021
Abstract
Environmental and public health research has given considerable attention to the impact of air quality on brain health, with systematic reviews being widespread. No literature review has been conducted for cognitive frailty—a multidimensional syndrome combining physical frailty and cognitive impairment and their apparent [...] Read more.
Environmental and public health research has given considerable attention to the impact of air quality on brain health, with systematic reviews being widespread. No literature review has been conducted for cognitive frailty—a multidimensional syndrome combining physical frailty and cognitive impairment and their apparent co-dependence, linked to increased vulnerability and adverse health outcomes, including dementia. Instead, cognitive decline and frailty are implicitly explored through research on air quality and comorbid cognitive and physical decline in elderly populations. A scoping review was conducted to explore the need for a systematic review. Combining the Arksey and O’Malley, and PRISMA-ScR checklist, a scoping review of SCOPUS using ‘cogniti*’ + ‘resilience’ + ‘air quality’ or ‘cogniti*’ + ‘ageing’ + ‘air quality’ resulted in n = 2503 articles, screened and reduced using inclusion and exclusion criteria, to n = 16 articles. Air quality appears to be a critical risk factor for cognitive decline, even at air quality levels below WHO targets. Moderate long-term ambient air pollution appears linked to increased risk of cognitive frailty, suggesting earlier and more active interventions to protect older people. There are varied effects on cognition across the life course, with both emotional and functional impacts. Effects may be more detrimental to elderly people with existing conditions, including economic and health inequalities. Generalisation of results is limited due to the absence of a dose–response, variations in methods, controlling for comorbid effects, and variance across studies. No literature review has been performed for cognitive frailty, largely due to the fact that it is not presently treated as an explicit outcome. The findings support the need for more research and a more extensive summary of the literature but suggest that there is worsening cognitive function over the life course as a result of increased PM2.5 concentrations. Furthermore, air quality appears to be a critical risk factor even at levels below World Health Organisation targets. Full article
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31 pages, 1095 KB  
Article
Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form
by Christophe Chesneau
Modelling 2023, 4(2), 102-132; https://doi.org/10.3390/modelling4020008 - 29 Mar 2023
Cited by 3 | Viewed by 2448
Abstract
Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based [...] Read more.
Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper. Full article
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9 pages, 241 KB  
Article
On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems
by Savin Treanţă
Mathematics 2021, 9(13), 1473; https://doi.org/10.3390/math9131473 - 23 Jun 2021
Cited by 9 | Viewed by 2133
Abstract
In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed [...] Read more.
In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
31 pages, 404 KB  
Review
Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials
by Jesús S. Dehesa
Entropy 2021, 23(5), 607; https://doi.org/10.3390/e23050607 - 14 May 2021
Cited by 8 | Viewed by 2219
Abstract
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is [...] Read more.
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state’s angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies–Thakkar, Lieb–Thirring, Redheffer–Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies. Full article
(This article belongs to the Special Issue Entropies, Divergences, Information, Identities and Inequalities)
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