Search Results (11,019)

This paper studies Dirichlet problems for one-dimensional Lévy-type nonlocal elliptic equations on the half-line. The equation $L^{\mu }\nu \left(x\right)=f\left(x\right),x>0,\nu \left(x\right)=0,x\le 0$ is transformed into a weighted nonlocal equation associated with a multiplicative jump process. Under basic structural assumptions on the Lévy measure, the transformed generator is realized through a martingale problem, and the associated exponential killing representation gives a probabilistic mild solution with an immediate $L^{\infty }$-estimate. For the one-dimensional fractional Laplacian, the transformed process is exactly multiplicative. This yields a new approach in which solution estimates are derived from the stochastic equation of the transformed process; smooth-data resolvent solutions are estimated in weighted $L_p$-spaces and extended to general data by approximation. For more general Lévy measures, a smooth weighted energy estimate is proved. The key analytic input is a weighted adjoint integral inequality for the transformed generator, verified for subordinate Brownian motions associated with Bernstein functions and for non-unimodal logarithmically perturbed stable-type operators. Full article

Monotonicity is a prevalent feature in natural language. Notably, determiners such as every, some, and no induce monotonic (upward) or antitonic (downward) entailments. The Monotonicity Calculus is a proof system that formalizes such reasoning in natural language inferences through order statements (inequalities) involving higher-order (typed) terms. In this paper, we prove that with a slight modification of the conditions for term formation, it is decidable over ground terms, i.e., terms that contain no variables. Full article

Complex conflict environments often involve composite conflicting parties composed of multiple individuals with divergent assessments, posing significant challenges for preference elicitation and conflict analysis in the Graph Model for Conflict Resolution (GMCR). Existing option prioritization methods in GMCR rely on ordinal rankings of statement importance and binary evaluations of state support, which limits their ability to capture nuanced and heterogeneous preferences. Moreover, current GMCR frameworks lack a systematic mechanism to reconcile divergent individual assessments and construct collective preferences. To address these gaps, this study integrates consensus-based group decision making into the GMCR framework through flexible assessments. Specifically, pairwise comparisons are employed to represent the relative importance of statements, while continuous values in [⁰,¹] are used to characterize the degree of statement support for states. To reconcile heterogeneous assessments, a minimum adjustment-based consensus reaching process is developed. Furthermore, grounded in inequity aversion theory from behavioral economics, fairness concern is incorporated to model individuals’ sensitivity to adjustment differences between themselves and others. Based on this mechanism, two minimum adjustment consensus models with fairness concern are proposed. The resulting consensus-based preferences are subsequently integrated into GMCR stability analysis to identify equilibrium solutions. A supply chain carbon reduction case is used to illustrate the implementation process and applicability of the proposed framework. Full article

This study examines how the composition of public education expenditure is associated with income inequality through educational quality and skill formation. While the existing literature largely focuses on aggregate education spending, this study argues that the allocation of resources across education levels plays a critical role in shaping educational outcomes and their distributional consequences. Using panel data for OECD countries over the period 2000–2022, we employ a simultaneous equation framework estimated using Three-Stage Least Squares (3SLS), complemented by a lag-structured empirical design and an instrumental-variable approach based on lagged expenditure to mitigate endogeneity concerns. The results reveal substantial heterogeneity across education levels. Tertiary education expenditure is positively associated with educational quality. Although its direct association with income inequality is not statistically significant, it exhibits a significant negative indirect association through the educational-quality channel. In contrast, spending at pre-primary, primary, and secondary levels exhibits weak or negative associations with measured learning outcomes and, in some cases, positive associations with income inequality. These patterns warrant cautious interpretation and may reflect diminishing marginal returns and endogenous policy responses in mature education systems. Further analysis suggests that educational quality serves as an important transmission mechanism linking education spending to income distribution, although no significant relationship is found with short-run economic growth, consistent with the long-term nature of human capital accumulation. Overall, the findings highlight the importance of improving the allocation and effectiveness of education spending rather than simply expanding aggregate budgets. Full article

This study examines how income inequality conditions the effectiveness of monetary policy in delivering sustainable economic growth in Saudi Arabia over 1980–2024, a question of direct relevance to the Kingdom’s Vision 2030 agenda and to Sustainable Development Goals 8 and 10. We apply an Autoregressive Distributed Lag (ARDL) bounds-testing framework to four monetary policy instruments—the Saudi Central Bank (SAMA) repo rate, broad money supply (M2), domestic credit to the private sector, and the real effective exchange rate (REER)—with the Gini coefficient introduced as a moderator through mean-centered interaction terms. The bounds test confirms a robust long-run cointegrating relationship, and the error-correction term indicates rapid adjustment to equilibrium. In the long run, interest rates exert a significant negative effect on growth and on trade openness, a positive effect, while income inequality significantly moderates the growth effects of broad money supply and private-sector credit. Diagnostic tests support the adequacy of the specification. The findings indicate that financial inclusion is not only a distributional objective but a macroeconomic prerequisite for effective monetary policy transmission, with direct implications for integrating inclusive-finance policy into the Vision 2030 framework. Full article

This paper investigates the problem of non-fragile dissipative filtering for discrete-time nonlinear networked systems with dynamic quantization, a dynamic event-triggered mechanism and stochastic cyber attacks. The nonlinear networked system under investigation is described by an uncertain Takagi–Sugeno (T-S) fuzzy model. In this work, a novel fuzzy-dependent dynamic event-triggered communication scheme and the dynamic quantization strategy, integrated with an online adjustment rule, are introduced to reduce the frequency and volume of data transmission, thus realizing more rational utilization of the limited communication resources. In addition, the stochastic cyber attacks are characterized by a random variable obeying the Bernoulli distribution. The core focus of this paper is to design a non-fragile filter such that the resulting filtering error system is stochastically stable and meets the prescribed dissipative filtering performance. Based on the matrix inequality decoupling technique, the design conditions of the desired filter are derived and presented in the form of linear matrix inequalities (LMIs). Finally, the effectiveness and superiority of the proposed filter design approach is verified via two simulation examples. Full article

Christian ethics are often associated with dichotomies such as right versus wrong, good versus evil, and moral versus immoral. How do young Black people with diverse sexual identities who also embrace Christianity understand such ethics? What constitutes Christian ethics for people who live on the margins and are often vilified for their racial and sexual identities? This mixed-methodological study considers these questions for a group of 76 young Black members of the LGBTQIA community aged 18–30 years old. The study is also designed to theorize and apply the concept of everyday sacredness as an ethos to illuminate the religious and spiritual experiences of Black sexual minorities. Three themes emerge that focus on ethical expectations. The initial theme reflects common questions about historic and present-day unethical practices in certain Black churches linked to homophobia and heterosexism found in current studies. The second, more spiritually focused theme, presents agape love as an ethical response to all God’s creation. The final practically focused theme emphasizes holistic health as an ethical response to health inequities in the Black LGBTQIA community. Full article

Background/Objectives: One contemporary problem in health economics is the measurement and interpretation of socioeconomic inequalities in outcomes, utilisation, and resource distribution. This article aims to estimate socioeconomic inequality in the regional allocation of health resources in Bulgaria during 2019–2023. Methods: A year-by-year database was created. It includes regions (n = 28), population, GDP per capita, and the numbers of practicing physicians, dentists, nurses, midwives, hospital beds, and outpatient facilities. Income inequality is analysed using decile ratios, the Gini coefficient, the Generalised Entropy index, and the Atkinson index. Socioeconomic health inequality is quantified using the concentration index (CI) and the coefficient of variation (CV) of the absolute number and of resource density (per 1000 inhabitants). The socio-economic variable is a regional gross domestic product (GDP) per capita fractional rank and a frequency-weight approach to account for population size is used. The analysis is extended with the relative and slope indices of inequality. The CI of hospital beds, practicing physicians, and nurses is decomposed using the age dependency ratio and the number of hospitalisations by districts. Results: The Gini index levels remain stable, with no significant fluctuations, in the narrow range of 29.6–29.7. The highest inequality of the absolute resource’s quantity is among midwives (Mean CI = 0.498, CV = 0.018), and the lowest among nurses (Mean CI = 0.442, CV = 0.024). For material resources, a greater concentration of outpatient organisations in richer areas is observed (Mean CI = 0.481, CV = 0.035) than for hospital beds (Mean CI = 0.427, CV = 0.034). The dynamics and descriptives of inequality of resources’ density follow the same pattern, but with lower average rates, ranging from 0.045 to 0.112. The obtained estimates are statistically significant (p < 0.05). The analysis of the regression-based measures confirms, without any doubt, both the magnitude and the direction of the development of inequalities in the territorial distribution of health resources. Conclusions: Inequality measures vary by resource group. Significant inequality exists in the distribution of health resources between poorer and richer regions, particularly in material resources, in the outpatient sector. For most resource groups, a very slight decrease in inequality is observed midway through the analysed period. The most significant part of this inequality can be explained by differences in hospital care and income across richer and poorer regions. Full article

This paper investigates the problem of exponential synchronization for a class of quaternion-valued inertial neural networks with mixed time delays under aperiodic intermittent control. First, a neural network model incorporating both discrete and distributed delays is established. To overcome the limitations of conventional approaches, a novel quaternion-based controller is proposed, which operates without relying on model order reduction or quaternion decomposition techniques, thereby achieving global exponential synchronization of the system. Furthermore, by constructing an appropriate Lyapunov function and combining the algebraic properties of quaternions with inequality techniques, sufficient conditions for synchronization are rigorously derived within the Lyapunov stability framework. Numerical simulations are conducted to demonstrate the effectiveness of the proposed control strategy and validate the theoretical results. Finally, an image encryption application is developed to further corroborate the practical viability of the proposed scheme, wherein the original image is encrypted into a noise-like pattern without information leakage and perfectly recovered upon synchronization, with quantitative error analysis confirming high-precision exponential synchronization. Full article

Artificial intelligence (AI) is increasingly embedded in development systems, enabling new capabilities for poverty prediction, social protection targeting and service delivery optimisation. However, the implications of these technologies for poverty governance—the institutional mechanisms for designing and delivering poverty reduction strategies—remain fragmented in the literature. This study conducted a PRISMA 2020-guided systematic review of peer-reviewed journal articles and scholarly book chapters published between 2015 and 2025 and retrieved from Scopus, Web of Science and DOAJ. Following title/abstract screening, full-text eligibility assessment and quality appraisal, 48 studies were selected, thematically identifying cross-cutting patterns related to system performance, implementation processes, governance considerations and contextual constraints. The reviewed literature indicates that AI can improve poverty governance through multimodal data integration, enhanced targeting accuracy and automated administrative processes. However, persistent challenges include biased datasets, infrastructural limitations, regulatory gaps and ethical risks such as algorithmic bias and digital exclusion, which may reinforce structural inequalities. The review contributes an integrated evidence base and introduces a conceptual framework for understanding AI in poverty governance, highlighting that developmental gains depend on robust data governance, inclusive digital infrastructure, context-sensitive design, algorithmic transparency and institutional capacity. Future research should prioritise impact evaluation, fairness-aware AI, participatory design and scalable approaches for low-resource environments. Full article

Quantum processes with indefinite causal order challenge the classical assumption that operations must occur in a single fixed temporal sequence. The quantum switch provides a concrete setting in which two operation orders, $A\prec B$ and $B\prec A$, are coherently controlled by a quantum system. In the strict process matrix formulation of the lazy guess your neighbour’s input (LGYNI) game, however, quantum theory, including the quantum switch, does not violate the standard causal inequality when probabilities are computed solely from local instruments. In this work, we study an extended control-assisted operational protocol in which the control system of the quantum switch is measured and used to define the task output. We compare increasingly expressive strategy classes, including single-qubit SU(2) operations, product target-ancilla operations, and entangling Cartan-decomposed two-qubit operations with generalized POVMs. Restricted models saturate or remain below the $3/4$ fixed-order benchmark, whereas the optimized Cartan + ancilla + POVM strategy reaches $P_{\mathrm{s}\mathrm{u}\mathrm{c}\mathrm{c}}^{\mathrm{e}\mathrm{x}\mathrm{t}}\approx 0.83596$, demonstrating enhanced task performance within the extended protocol. The optimized strategy remains operationally no-signaling to numerical precision and retains its extended protocol advantage under more than $25\mathrm{\%}$ white noise admixture. These results identify the operational resources required for control-assisted quantum switch enhancement and support the view that indefinite temporal order can be used as a quantum informational resource without implying a breakdown of operational causality. Full article

This study developed an integrated stochastic framework to forecast cotton pest outbreaks across six tropical Indian agroecosystems. Methodologically, the approach fused entropy and Gini inequality indices, Random Forest machine learning, SHAP-based feature interpretation, fuzzy logic risk assessment, and climate scenario simulations (+2 °C, +20% rainfall) to quantify outbreak variability, driver importance, and system resilience. Findings revealed extreme pest stochasticity (mean = 15.7, variance > 4200), with low entropy (0.06) and a high Gini coefficient (0.82) confirming highly concentrated spatial and temporal outbreaks. While Random Forest demonstrated limited predictive skill (RMSE = 68.9, R² = 0.07), SHAP analysis transparently identified evaporation, wind speed, and humidity as dominant drivers. Fuzzy logic yielded an average risk score of 1.0, reflecting frequent exceedance of biological thresholds. Scenario simulations demonstrated pronounced climate sensitivity: a +2 °C temperature increase raised mean incidence to 18.7, and +20% rainfall increased it to 18.6, resulting in a resilience index of 1.51 that indicates disproportionate vulnerability. In conclusion, combining stochastic variability metrics, explainable machine learning, and threshold-based risk modeling significantly advances tropical pest forecasting under uncertainty. Importantly, this framework contributes to sustainability by enabling climate-resilient cotton production, reducing reliance on chemical pesticides, and supporting adaptive advisory systems that strengthen long-term agroecosystem resilience. These results emphasize the critical need for adaptive, location-specific management strategies to mitigate climate-driven pest intensification and enhance resilience in cotton production systems. Full article

This paper investigates the synchronization problem for a class of proportional Caputo fractional-order neural networks with respect to another function. A master–slave framework is formulated, and a linear state-feedback controller is proposed for the response system. Under a standard Lipschitz condition on the activation functions, sufficient conditions ensuring the convergence of the synchronization error to zero are established. The analysis is based on an explicit integral representation of the error system, a generalized Gronwall-type inequality, and asymptotic properties of the Mittag–Leffler function. The obtained criterion explicitly reveals the roles of the fractional order, the proportional parameter, the control gain, and the network interconnection matrix. Numerical experiments based on a benchmark fractional Hopfield neural network illustrate the effectiveness of the proposed approach. In particular, a scaled benchmark satisfying all theoretical assumptions provides a strict validation of the main theorem, while the original benchmark highlights the conservative nature of the derived sufficient conditions. Full article

In this study, we examine the persistence of gendered inequality in unpaid domestic work among employed individuals during Thailand’s 2004–2014 structural transformation, a period shaped by major reforms in education and healthcare. We provide new evidence from middle-income Southeast Asia, where gender norms remain strong but empirical evidence is still limited, especially for marriage and labor market segregation. Methodologically, we use repeated cross-sectional data from Thailand’s Time Use Survey (N = 57,555) and pooled OLS models with survey-year fixed effects under alternative sample definitions. Our results reveal a large and persistent gender gap across all specifications. Marriage is associated with substantially higher amounts of unpaid domestic work for women, while labor market segregation displays gendered dynamics: employment in female-dominated industries and female household headship are associated with lower domestic work burdens, whereas employment in male-dominated industries shows no robust association with women’s unpaid domestic work time. Although the raw gender gap narrowed over the ten-year period, the adjusted gap widened after accounting for individual, employment, and household characteristics, suggesting that compositional improvements among women masked a deepening relative domestic burden. These findings suggest that economic development alone may not automatically reduce gender inequality within households, with important implications for labor markets and social policies in developing economies. Full article

This paper introduces a novel, domain-independent methodology for risk reduction based on the reverse engineering of sub-additive inequalities. The proposed approach establishes a robust and unifying theoretical framework for risk reduction that is applicable across a broad range of otherwise unrelated domains. As part of the methodology, a general sub-additive inequality is formulated and rigorously proved, together with sufficient conditions for its validity. The analysis demonstrates that, for the inequality to be reverse engineered, both the risk-controlling parameter and the measure of risk must be additive quantities. Several important special cases of general inequality are derived, and the influence of segmentation on risk reduction has been examined. The practical applicability of the proposed framework is demonstrated through diverse examples, including the reduction in expected failures through optimized inspection, mitigation of corrosion damage and environmental pollution, prevention of runaway reactions, enhancement of cutting tool reliability, and optimization of dose distribution to reduce health risks. Full article