Search Results (1,851)

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

Introduction: Dental caries and molar–incisor hypomineralisation (MIH) are prevalent conditions affecting children’s oral health, with functional, aesthetic, and psychosocial implications. In Spain, previous studies have highlighted geographic and sociodemographic disparities in their distribution, particularly among rural and migrant populations. Objective: To characterise oral health status, in terms of caries and MIH, among 6–7-year-old children from the towns of Palos de la Frontera, Mazagón, and San Bartolomé. Methods: A cross-sectional study was conducted involving 229 children recruited from public primary schools. Sociodemographic, anthropometric, and behavioural data were collected through clinical examination and interview. Statistical analysis included univariate and multivariate logistic regression. The study protocol was approved by the Ethics Committee of Huelva. Results: The prevalence of caries (DMFT ≥ 1) was 53.3%, with mean DMFT and dft indices of 1.78 and 0.31, respectively. MIH affected 32.8% of the cohort, with a predominance in the first permanent molars (teeth 36 and 26). Multivariate analysis identified independent predictors of caries: African (OR = 7.47; 95% CI: 2.84–23.8) and European (OR = 4.56; 95% CI: 1.26–22.3) parental origin, poor oral hygiene (OR = 3.07; 95% CI: 1.60–6.03), and the presence of MIH (OR = 3.20; 95% CI: 1.64–6.42). The municipality of San Bartolomé was associated with a higher risk of MIH (OR = 2.90; 95% CI: 1.21–7.45). Conclusions: The high prevalence of caries and MIH in the Condado-Campiña district, exceeding national averages, reflects oral health inequities linked to social determinants (migrant origin, locality) and clinical factors (MIH, oral hygiene). Targeted preventive interventions are urgently needed in high-risk populations, including culturally tailored education and policies ensuring equitable access to dental care services. Full article

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

Substance use is a critical public health issue in the U.S., with Black communities, particularly those with criminal justice contact, disproportionately affected. Chronic exposure to stressors can lead to substance use as a coping strategy. This study used data from 1476 Black adults with criminal justice involvement from the National Survey of American Life to examine how psychosocial stress and sleep disturbances relate to lifetime substance use and to determine if there are any sex differences. Sex-separate generalized linear models for a Poisson distribution with a log-link function estimated prevalence ratios and adjusted prevalence ratios (APRs) for lifetime alcohol abuse, lifetime cigarette, and marijuana use. Independent variables include stressors (family, person, neighborhood, financial, and work-related) and sleep problems, with covariates such as age, SES, and marital status. Lifetime alcohol abuse was associated with family stressors (APR = 2.72) and sleep problems (APR = 3.36) for males, and financial stressors (APR = 2.75) and sleep problems (APR = 2.24) for females. Cigarette use was linked to family stressors (APR = 1.73) for males and work stressors (APR = 1.78) for females. Marijuana use was associated with family stressors (APR = 2.31) and sleep problems (APR = 2.07) for males, and neighborhood stressors (APR = 1.72) for females. Lifetime alcohol abuse, as well as lifetime cigarette and marijuana use, was uniquely associated with various psychosocial stressors among Black adult males and females with criminal justice contact. These findings highlight the role of structural inequities in shaping substance use and support using a Social Determinants of Health framework to address addiction in this population. Full article

A refined version of the q-Hermite–Hadamard inequalities for strongly convex functions is introduced in this paper, utilizing both left and right q-integrals. Tighter bounds and more accurate estimates are derived by incorporating strong convexity. New q-trapezoidal and q-midpoint estimates are also presented to enhance the precision of the results. The improvements in the results compared to previous work are demonstrated through numerical examples in terms of precision and tighter bounds, and the advantages of using strongly convex functions are showcased. Full article

The establishment and management of nature reserves play a crucial role in protecting biodiversity and supporting sustainable agriculture. This study focuses on 2538 nature reserves in 22 provinces, 5 autonomous regions and 4 municipalities directly under the central government in mainland China. Integrating GIS spatial statistics, imbalance index, and geodetector models, we reveal critical insights: (1) Pronounced spatial inequity is observed, where a small number of eastern provinces dominate the total reserve count, highlighting significant regional disparities in ecological resource allocation. The sparse kernel density in western regions, indicating sparse reserve coverage. The Standard Deviation Ellipse highlights directional dispersion and human-ecological conflicts in high-density zones. (2) Key sustainability indicators driving reserve distribution include: total water resources, water resources per capita, forest area. (3) The spatial distribution of China’s nature reserves, along with factors such as altitude, river distribution, and transportation infrastructure, plays a crucial role in their development. This research provides theoretical support for the scientific planning and policy-making of nature reserves in China and offers practical guidance for optimizing and adjusting sustainable agricultural development. The study emphasizes the vital functions of nature reserves in maintaining ecosystem balance, enhancing regional climate resilience, and serving as biodiversity reservoirs. This research offers strategic insights for integrating nature reserve spatial planning with sustainable agricultural development policies, providing a scientific basis for optimizing the eco-agricultural interface in China. Full article

In this paper, we generalize an inequality for a convex function in one dimension ${\mathbb{R}}^1$ on three intervals to a function with nondecreasing increments in k dimensions ${\mathbb{R}}^k$ on $(2n+1)$ intervals. We prove all the situations when $n=1,2$ and prove a very special case for a general n as well as the discrete version. The proofs are based on a general conclusion for convex functions, and analogues of this conclusion are established. We apply the discrete case of the inequality to Csiszár $\varphi$-divergence $I_{\varphi }(p,q)$ in information theory, and the continuous case $I_{\varphi }(p_1,q_1)\le I_{\varphi }(p_2,q_2)$ on a measurable set is also established. The same inequality for an $ϵ$-approximately convex function on a discrete set is also established and can be used to prove a similar Landau–Kolmogorov-type inequality. Full article

In an era marked by accelerating ecological degradation and widening global inequalities, prevailing patterns of resource extraction and consumption are proving increasingly unsustainable. Driven by hyper-consumption and entrenched linear production models, the global economy continues to exert immense pressure on planetary systems. This communication article calls for a fundamental paradigm shift from the long-standing assumption of resource abundance to a framework of responsible scarcity. Drawing from recent data on material throughput, on the transgression of planetary boundaries, and on the structural and geopolitical disparities underlying global resource use, this article highlights the urgent need to realign natural resource governance with ecological limits and social justice. A conceptual framework is proposed to support this transition, grounded in principles of ecological constraint, functional sufficiency, equity, and long-term resilience. The article concludes by outlining a forward-thinking research and policy agenda aimed at fostering sustainable and just modes of resource utilization in the face of growing environmental and socio-economic challenges. Full article

This study examines how U.S. immigration policies enact legal violence and multigenerational punishment through the spousal reunification process, particularly in mixed-status, transnational families. Building on the concept of “deportability,” we introduce “importability” to describe a beneficiary’s potential to secure permanent residency, which varies according to social markers such as race, gender, and region of origin. Drawing from a content analysis of threads on the Immigration Pathways (IP) web forum, we analyze discussions among U.S. citizen petitioners navigating marriage-based green card applications, with a focus on experiences involving administrative processing (AP) (i.e., marriage fraud investigations). Our findings show that couples who do not align with the state’s conception of “proper” family—particularly U.S. citizen women petitioning for Black African partners—face intensified scrutiny, long delays, and burdensome requirements, including DNA tests and surveillance. These bureaucratic obstacles produce prolonged family separation, financial strain, and diminished sense of belonging, especially for children in single-parent households. Through the lens of “importability,” we reveal how legal violence and multigenerational punishment of immigration policies on mixed-status families beyond deportation threats, functioning as a gatekeeping mechanism that disproportionately affects marginalized families. This research highlights the understudied consequences of immigration policies on citizen petitioners and contributes to a broader understanding of inequality in U.S. immigration enforcement. Full article

This study explores the spatial and social implications of urban food systems in Quito, Ecuador, focusing on how food access inequalities reflect and reinforce broader urban disparities. The research addresses a critical problem in contemporary urbanization: the disconnection between food provisioning and spatial equity in rapidly growing cities. The objective is to assess and map disparities in food accessibility using a mixed-methods approach that includes field observation, participatory mapping, value chain analysis, and statistical modeling. Five traditional and emerging food markets were studied in diverse districts across the city. A synthetic accessibility function F(x) was constructed to model food access levels, integrating variables such as income, infrastructure, transport availability, and travel time. These variables were subjected to Principal Component Analysis (PCA) and hierarchical clustering to generate three typologies of territorial vulnerability. The results reveal that peripheral areas exhibit lower F(x) values and weaker integration with the formal food system, leading to higher consumer costs and limited fresh food options. In contrast, central districts benefit from multimodal infrastructure and greater diversity of supply. This study concludes that food systems should be treated as critical urban infrastructure. Integrating food equity into land use and mobility planning is essential to promote inclusive, sustainable, and resilient urban development. Full article

This paper investigates the problem of identifying a time-dependent source term in distributed-order time-space fractional diffusion equations (FDEs) based on boundary observation data. Firstly, the existence, uniqueness, and regularity of the solution to the direct problem are proved. Using the regularity of the solution and a Gronwall inequality with a weakly singular kernel, the uniqueness and stability estimates of the solution to the inverse problem are obtained. Subsequently, the inverse source problem is transformed into a minimization problem of a functional using the Tikhonov regularization method, and an approximate solution is obtained by the conjugate gradient method. Numerical experiments confirm that the method provides both accurate and robust results. Full article

Most image forgery localization methods rely on supervised learning, requiring large labeled datasets for training. Recently, several unsupervised approaches based on the variational autoencoder (VAE) framework have been proposed for forged pixel detection. In these approaches, the latent space is built by a simple Gaussian distribution or a Gaussian Mixture Model. Despite their success, there are still some limitations: (1) A simple Gaussian distribution assumption in the latent space constrains performance due to the diverse distribution of forged images. (2) Gaussian Mixture Models (GMMs) introduce non-convex log-sum-exp functions in the Kullback–Leibler (KL) divergence term, leading to gradient instability and convergence issues during training. (3) Estimating GMM mixing coefficients typically involves either the expectation-maximization (EM) algorithm before VAE training or a multilayer perceptron (MLP), both of which increase computational complexity. To address these limitations, we propose the Deep ViT-VAE-GMM (DVVG) framework. First, we employ Jensen’s inequality to simplify the KL divergence computation, reducing gradient instability and improving training stability. Second, we introduce convolutional neural networks (CNNs) to adaptively estimate the mixing coefficients, enabling an end-to-end architecture while significantly lowering computational costs. Experimental results on benchmark datasets demonstrate that DVVG not only enhances VAE performance but also improves efficiency in modeling complex latent distributions. Our method effectively balances performance and computational feasibility, making it a practical solution for real-world image forgery localization. Full article

This study investigates the impact of remittances on income inequality in Lebanon using annual time-series data for the years 2000–2023. Applying Johansen’s cointegration test, with financial development (FD), GDP, and household consumption expenditure (HCE) as the control variables, the study examines the long-run and short-run relationship between remittances and inequality. The study also considers the moderating impacts of FD and HCE to account for their indirect role in the remittance–inequality relationship. Dynamic relations are also examined by using impulse response functions (IRFs) and Forecast Error Variance Decomposition (FEVD) analyses. The long-run model estimates validate that remittances and income inequality are significantly and negatively related, i.e., increased remittance receipts serve to reduce income inequality in Lebanon. Remittance effects, however, are statistically insignificant in the short run. Interestingly, the results reveal that financial development weakens the remittances’ inequality-reducing effect, dampening their impact. Contrarily, a higher household consumption expenditure slightly strengthens the inequality-reducing effect of remittances. A comparison between the pre- and post-2019 periods reveals that the explanatory strength of remittances weakened during times of economic crisis, since the function of remittances was different during times of economic distress. Based on these findings, this study recommends that Lebanon not only promote financial development but also focus on financial inclusion, improve social safety nets, and provide inclusive economic growth to maximize remittance inflow benefits and efficiently reduce inequality. Full article

This paper investigates a new class of fractional integral operators, namely, the exponentially damped Riesz-type operators within the framework of variable exponent Lebesgue spaces $L^{\mathtt{p}(·)}$. To the best of our knowledge, the boundedness of such operators has not been addressed in any existing functional setting. We establish their boundedness under appropriate log-Hölder continuity and growth conditions on the exponent function $\mathtt{p}(·)$. To highlight the novelty and practical relevance of the proposed operator, we conduct a comparative analysis demonstrating its effectiveness in addressing convergence, regularity, and stability of solutions to partial differential equations. We also provide non-trivial examples that illustrate not only these properties but also show that, under this operator, a broader class of functions becomes locally integrable. The exponential decay factor notably broadens the domain of boundedness compared to classical Riesz and Bessel–Riesz potentials, making the operator more versatile and robust. Additionally, we generalize earlier results on Sobolev-type inequalities previously studied in constant exponent spaces by extending them to the variable exponent setting through our fractional operator, which reduces to the classical Riesz potential when the decay parameter $\lambda =0$. Applications to elliptic PDEs are provided to illustrate the functional impact of our results. Furthermore, we develop several new structural properties tailored to variable exponent frameworks, reinforcing the strength and applicability of the proposed theory. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article