Search Results (690)

In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms. Full article

In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxiliary variable $\sigma =\Delta u$, the original fourth-order model is reformulated into a lower-order coupled system. The first-order time derivative and the time fractional derivative are discretized by using the BDF2 formula and the weighted and shifted Grünwald difference (WSGD) formula, respectively. Then, a fully discrete MFVE scheme is constructed by using the primal and dual grids. The existence and uniqueness of a solution for the MFVE scheme are proven based on the matrix theories. The scheme’s unconditional stability is rigorously derived by using the Gronwall inequality in detail. Moreover, the optimal error estimates for u in the discrete $L^{\infty }\left(L^2(\Omega )\right)$ and $L^2\left(H^1(\Omega )\right)$ norms and for $\sigma$ in the discrete $L^2\left(L^2(\Omega )\right)$ norm are obtained. Finally, three numerical examples are given to confirm its feasibility and effectiveness. Full article

Traditional antenna arrays for direction-of-arrival (DOA) estimation typically require numerous elements to achieve target performance, increasing system complexity and cost. Reconfigurable intelligent surfaces (RISs) offer a promising alternative, yet their performance critically depends on phase coding design. To address this, we propose a phase coding design method for RIS-aided DOA estimation with a single receiving channel. First, we establish a system model where averaged received signals construct a power-based formulation. This transforms DOA estimation into a compressed sensing-based sparse recovery problem, with the RIS far-field power radiation pattern serving as the measurement matrix. Then, we derive the decoupled expression of the measurement matrix, which consists of the phase coding matrix, propagation phase shifts, and array steering matrix. The phase coding design is then formulated as a Frobenius norm minimization problem, approximating the Gram matrix of the equivalent measurement matrix to an identity matrix. Accordingly, the phase coding design problem is reformulated as a Frobenius norm minimization problem, where the Gram matrix of the equivalent measurement matrix is approximated to an identity matrix. The phase coding is deterministically constructed as the product of a unitary matrix and a partial Hadamard matrix. Simulations demonstrate that the proposed phase coding design outperforms random phase coding in terms of angular estimation accuracy, resolution probability, and the requirement of coding sequences. Full article

The historical peak in CO₂ emissions has intensified global environmental concerns, urging the identification of key determinants. While economic drivers are well-documented, political dimensions—especially democracy and institutional quality—are increasingly emphasized. However, the role of freedom of association and organization (AOF), a core democratic element, remains largely unexamined in this context. This study fills this gap by analyzing the impact of AOF on CO₂ emissions in the top 20 emitter countries from 2006 to 2022. The selection of these countries enables a focused assessment of the world’s primary polluters, ensuring high policy relevance. Using second-generation panel estimators, the Augmented Mean Group and the Common Correlated Effects Mean Group estimators, the analysis accounts for heterogeneity and cross-sectional dependence. Robustness is tested using the CS-ARDL method, confirming the stability of results. Empirical findings show that higher levels of AOF significantly reduce CO₂ emissions. Income and energy consumption increase emissions, while the effect of trade openness is statistically insignificant. These results suggest that strengthening associational freedoms can offer a dual benefit: advancing democratic norms and achieving environmental goals. Full article

Sub-Saharan Africa’s (SSA) corporate environment, like many emerging markets, is marked by institutional voids, weak oversight structures, and patriarchal leadership norms, which heighten the risk of real earnings management (REM). This study examines how CEO characteristics and audit committee gender diversity influence REM among listed manufacturing firms in 12 SSA countries from 2012 to 2023. Anchored in agency theory and Upper Echelon Theory, this study draws on 1189 firm-year observations and employs Pooled OLS, Random Effects, Fixed Effects, Feasible Generalised Least Squares (FGLS), and System GMM estimators. Findings show that female CEOs are consistently associated with lower REM, underscoring the ethical conservatism linked to gender-inclusive leadership. CEO ownership shows a positive and significant association with REM in System GMM, though findings vary across models, indicating potential institutional effects. The firm size is negatively and significantly related to REM in Pooled, RE, and FGLS models, but becomes nonsignificant in FE and System GMM, suggesting the role of external scrutiny may be sensitive to model dynamics. Leverage exhibits a positive and significant relationship with REM in most models, but turns negative and nonsignificant under System GMM, pointing to endogeneity concerns. Interaction effects and country-specific regressions affirm that governance impacts differ across contexts. Policy reforms should prioritise gender-diverse leadership and tailored oversight mechanisms. Full article

This study examines whether China’s rapid spread of internet and mobile information technologies has translated into greater household support for government air-quality programs. Using nationally representative data from the Chinese General Social Survey (2018), this study estimates the causal impact of digital media use on residents’ willing to pay (WTP) each month for one additional “good-air” day. Ordinary least squares shows that individuals who rely primarily on the internet or mobile push services are willing to contribute CNY 1.9–2.7 more—about 43 percent above the sample mean of CNY 4.41. To address potential endogeneity, we instrumented digital media adoption using provincial computer penetration; two-stage least squares yielded roughly CNY 10.5, confirming a causal effect. Mechanism tests showed that digital access lowers complacency about local air quality, strengthens anthropogenic attribution of pollution, and heightens the moral norm that economic sacrifice is legitimate, jointly mediating the rise in WTP. Heterogeneity analyses revealed stronger effects among high-income households and renters, while extended tests showed that (i) the impact intensifies when the promised environmental gain rises from one to three or five clean-air days, (ii) attention to international news can crowd out local WTP, and (iii) digital media raise not only the likelihood of paying but also the amount paid among existing contributors. The findings suggest that targeted digital outreach—especially messages with concrete, locally salient goals—can substantially enlarge the fiscal base for air-quality initiatives, helping China advance its ecological-civilization and dual-carbon objectives. Full article

This paper addresses the problem of target localization in a distributed waveform diverse array radar system, exploiting the technique of sparse reconstruction. At the configuration stage, the distributed radar system consists of two individual Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radars and one single Element-Pulse Coding MIMO (EPC-MIMO) radar. To obtain the angle and incremental range (i.e., the range offset between the sampling point and actual position within the range bin) of the targets in each local radar, two sparse reconstruction-based algorithms, including the grid-based Iterative Adaptive Approach (IAA) and gridless Atomic Norm Minimization (ANM) algorithms, are implemented. Furthermore, multiple sets of local statistics are fused at the fusion center, where a Weighted Least Squares (WLS) method is performed to localize targets. At the analysis stage, the estimation performance of the proposed methods, encompassing both IAA and ANM algorithms, is evaluated in contrast to the Cramér–Rao Bound (CRB). Numerical results and parametric studies are provided to demonstrate the effectiveness of the proposed sparse reconstruction methods for target localization in the distributed waveform diverse array system. Full article

Background: Over the last 30 years, stress and anxiety in children have risen exponentially, especially as a result of school expectations. As no studies have examined the effect of increased outdoor recess on children’s chronic stress levels, this preliminary work focused on comparing hair cortisol concentration (HCC) scores of elementary children who received varied amounts of daily recess. Methods: HCC scores were collected from 4th grade elementary children (N = 130) from three intervention schools (45 min daily recess) (N = 64; M = 35; F = 29) and three control schools (30 min daily recess) (N = 66; M = 31; F = 35). Results: A two-way ANOVA, F(1, 123) = 5.47, p = 0.021, ω² = 0.034, showed that the intervention group reflected lower HCC levels (marginal M = 5.69, 95% CI [−1.92, 13.30]) than the control group (marginal M = 18.22, 95% CI [10.83, 25.61]). Post hoc analysis revealed an estimated marginal mean difference of −12.53 (SE = 5.36, p = 0.021). Sample t-tests compared HCC levels against the pre-COVID normative value of 7.5 pg/mg. The intervention group HCC mean (M = 5.85, SD = 6.26) was significantly lower than the normative value, t(61) = −2.08, p = 0.042. The control group’s mean HCC (M = 18.22, SD = 41.39) was significantly higher than the normative value, t(64) = 2.09, p = 0.041. Conclusions: Increasing daily recess may contribute to lower chronic stress levels among 4th grade children. With obesity and mental health disorders on the rise and American students’ academic performance on the decline, these pilot results cannot be overlooked or dismissed. Full article

A biharmonic boundary value problem with a singularity is one of the mathematical models of processes in fracture mechanics. It is necessary to have estimates of the function norms in the neighborhood of the singularity point to study the existence and uniqueness of the $R_{\nu }$-generalized solution, its coercive and differential properties of biharmonic boundary value problems with a corner singularity. This paper establishes estimates of a function in the neighborhood of a singularity point in the norms of weighted Lebesgue spaces through its norms in weighted Sobolev spaces over the entire domain, with a minimum weight exponent. In addition, we obtain an estimate of the function norm in a boundary strip for the degeneration of a function on the entire boundary of the domain. These estimates will be useful not only for studying differential problems with singularity, but also in estimating the convergence rate of an approximate solution to an exact one in the weighted finite element method. Full article

The effects of initial institutions and change in institutions on the growth of ex-socialist countries is unsettled in the literature. This is due to difficulties in modeling the effects of institutions and their change. The objective of this paper is to contribute to this area. Ex-socialist countries faced heterogenous initial conditions at transition. Those that joined the EU experienced institutional integration as well as institutional improvement. Using publicly available data from about ten years before and after EU accession and two-way fixed effects differences-in-differences estimation, this paper finds that these countries experienced growth boosts post-EU accession. Achieving institutional integration cum improvement by accepting and implementing EU’s regulations and norms in all details permitted this boost. The initial conditions mattered—the effect was greater in “new” ex-socialist countries (which had the additional burden of creating new administrative structures and economic relationships) than in the “old.” Using the neo-classical growth model, the paper then examines whether this boost in growth was due to a higher contribution of inputs or due to an increase in the efficiency with which inputs were used. It indicates that it was due to increased contribution of human capital rather than an increase in the amount of human capital or other economic or political confounders. These countries’ skilled labor, already high in skills at transition by OECD standards, needed the right institutions to unlock its potential. Full article

Maintaining a spacecraft’s center of mass at the origin of a body-fixed coordinate system is often key to precision trajectory tracking. Typically, the inertia matrix is estimated and verified with preliminary ground testing. This article presents groundbreaking preliminary results and significant findings from on-orbit space experiments validating recently proposed methods as part of a larger study over multiple years. Time-varying estimates of inertia moments and products are used to reveal time-varying estimates of the location of spacecraft center of mass using geosynchronous orbiting test satellites proposing a novel two-norm optimal projection learning method. Using the parallel axis theorem, the location of the mass center is parameterized using the cross products of inertia, and that information is extracted from spaceflight maneuver data validating modeling and simulation. Mass inertia properties are discerned, and the mass center is experimentally revealed to be over thirty centimeters away from the assumed locations in two of the three axes. Rotation about one axis is found to be very well balanced, with the center of gravity lying on that axis. Two-to-three orders of magnitude corrections to inertia identification are experimentally demonstrated. Combined-axis three-dimensional maneuvers are found to obscure identification compared with single-axis maneuvering as predicted by the sequel analytic study. Mass center location migrates 36–95% and subsequent validating experiments duplicate the results to within 0.1%. Full article

Although the transition to electric vehicles (EVs) is well underway and expected to continue in global car markets, most vehicles on the world’s roads will be powered by internal combustion engine vehicles (ICEVs) and fossil fuels for the foreseeable future, possibly well past 2050. Thus, good environmental performance and effective emission control of ICE vehicles will continue to be of paramount importance if the world is to achieve the stated air and climate pollution reduction goals. In this study, we review 228 publications and identify four main issues confronting these objectives: (1) cheating by vehicle manufacturers, (2) tampering by vehicle owners, (3) malfunctioning emission control systems, and (4) inadequate in-service emission programs. With progressively more stringent vehicle emission and fuel quality standards being implemented in all major markets, engine designs and emission control systems have become increasingly complex and sophisticated, creating opportunities for cheating and tampering. This is not a new phenomenon, with the first cases reported in the 1970s and continuing to happen today. Cheating appears not to be restricted to specific manufacturers or vehicle types. Suspicious real-world emissions behavior suggests that the use of defeat devices may be widespread. Defeat devices are primarily a concern with diesel vehicles, where emission control deactivation in real-world driving can lower manufacturing costs, improve fuel economy, reduce engine noise, improve vehicle performance, and extend refill intervals for diesel exhaust fluid, if present. Despite the financial penalties, undesired global attention, damage to brand reputation, a temporary drop in sales and stock value, and forced recalls, cheating may continue. Private vehicle owners resort to tampering to (1) improve performance and fuel efficiency; (2) avoid operating costs, including repairs; (3) increase the resale value of the vehicle (i.e., odometer tampering); or (4) simply to rebel against established norms. Tampering and cheating in the commercial freight sector also mean undercutting law-abiding operators, gaining unfair economic advantage, and posing excess harm to the environment and public health. At the individual vehicle level, the impacts of cheating, tampering, or malfunctioning emission control systems can be substantial. The removal or deactivation of emission control systems increases emissions—for instance, typically 70% (NO_x and EGR), a factor of 3 or more (NO_x and SCR), and a factor of 25–100 (PM and DPF). Our analysis shows significant uncertainty and (geographic) variability regarding the occurrence of cheating and tampering by vehicle owners. The available evidence suggests that fleet-wide impacts of cheating and tampering on emissions are undeniable, substantial, and cannot be ignored. The presence of a relatively small fraction of high-emitters, due to either cheating, tampering, or malfunctioning, causes excess pollution that must be tackled by environmental authorities around the world, in particular in emerging economies, where millions of used ICE vehicles from the US and EU end up. Modernized in-service emission programs designed to efficiently identify and fix large faults are needed to ensure that the benefits of modern vehicle technologies are not lost. Effective programs should address malfunctions, engine problems, incorrect repairs, a lack of servicing and maintenance, poorly retrofitted fuel and emission control systems, the use of improper or low-quality fuels and tampering. Periodic Test and Repair (PTR) is a common in-service program. We estimate that PTR generally reduces emissions by 11% (8–14%), 11% (7–15%), and 4% (−1–10%) for carbon monoxide (CO), hydrocarbons (HC), and oxides of nitrogen (NO_x), respectively. This is based on the grand mean effect and the associated 95% confidence interval. PTR effectiveness could be significantly higher, but we find that it critically depends on various design factors, including (1) comprehensive fleet coverage, (2) a suitable test procedure, (3) compliance and enforcement, (4) proper technician training, (5) quality control and quality assurance, (6) periodic program evaluation, and (7) minimization of waivers and exemptions. Now that both particulate matter (PM, i.e., DPF) and NO_x (i.e., SCR) emission controls are common in all modern new diesel vehicles, and commonly the focus of cheating and tampering, robust measurement approaches for assessing in-use emissions performance are urgently needed to modernize PTR programs. To increase (cost) effectiveness, a modern approach could include screening methods, such as remote sensing and plume chasing. We conclude this study with recommendations and suggestions for future improvements and research, listing a range of potential solutions for the issues identified in new and in-service vehicles. Full article

Background: The Montreal Cognitive Assessment (MoCA) is widely used to evaluate global cognitive function; however, its precision in measurement in heterogeneous populations—especially among patients with Parkinson’s disease (PD)—remains underexplored. Methods: In this multicenter cross-sectional study, we examined the psychometric properties of the Brazilian Portuguese MoCA in 484 PD patients (age range, 26–90 years; mean ± SD, 59.9 ± 11.1 years; disease duration range, 1–35 years; mean ± SD, 8.7 ± 5.4 years) using Item Response Theory (IRT). The Graded Response Model (GRM) was employed to estimate item difficulty and discrimination parameters, and differential item functioning (DIF) concerning age and education was investigated via a Multiple Indicators Multiple Causes (MIMIC) model. Results: The MoCA demonstrated essential unidimensionality and robust model fit. GRM analyses revealed that items within the Attention and Naming domains had high discrimination, indicating sensitivity to subtle cognitive deficits, while Memory items exhibited lower discrimination. Orientation items showed low difficulty thresholds, suggesting a propensity for ceiling effects. The MIMIC model further indicated that age and education significantly influenced overall scores: increasing age was associated with lower performance, whereas higher educational attainment correlated with better outcomes, particularly in Memory Recall and Executive/Visuospatial domains, even after accounting for their modest inverse relationship. Conclusions: Our findings support the validity of the Brazilian Portuguese MoCA for cognitive screening in PD while highlighting item-level biases linked to age and education. These results advocate for using education-adjusted norms and computerized scoring algorithms that incorporate item parameters, ultimately enhancing the reliability and fairness of cognitive assessments in diverse clinical populations. Full article

This paper proposes a weak Galerkin (WG) finite element method for solving a multi-dimensional evolution equation with a weakly singular kernel. The temporal discretization employs the backward Euler scheme, while the fractional integral term is approximated via a piecewise constant function method. A fully discrete scheme is constructed by integrating the WG finite element approach for spatial discretization. $L^2$-norm stability and convergence analysis of the fully discrete scheme are rigorously established. Numerical experiments are conducted to validate the theoretical findings and demonstrate optimal convergence order in both spatial and temporal directions. The numerical results confirm that the proposed method achieves an accuracy of the order $O\left(\tau +h^{k+1}\right)$, where $\tau$ and h represent the time step and spatial mesh size, respectively. This work extends previous studies on one-dimensional problems to higher spatial dimensions, providing a robust framework for handling evolution equations with a weakly singular kernel. Full article

Some estimates suggest that one in seven good readers and the majority of children with reading difficulties suffer from oculomotor dysfunction (OMD), an umbrella term for abnormalities in comfortable and accurate fixations, pursuits, and saccades. However, national vision evaluation programs worldwide are often limited to distance visual acuity (dVA), not testing for OMD despite its high prevalence and the ease of detecting it in brief optometric evaluations. We hypothesized that reading acquisition is dependent on good oculomotor functions, and therefore inadequate oculomotor control will be associated with reading difficulties. We retrospectively examined and compared oculomotor evaluations (using DEM and NSUCO) and reading assessments (using standardized national reading norms) of a normative class (28 first graders (6–7 yr. olds)) that were independently obtained while blind to the other assessment. Better oculomotor performance as estimated by DEM was associated with better reading performance, and almost a third (29.6%) of the children were categorized by DEM as having OMD-related difficulties. Control analysis revealed dVA was not positively associated with reading performance. Linear regression analyses further corroborated these findings. Since this study is based on a small cohort and since there are studies suggesting that DEM may actually reflect visual processing speed or cognitive factors rather than oculomotor function, replications are needed to substantiate the direct contribution of oculomotor functions to reading acquisition. Young children struggling with reading may benefit from a comprehensive visual evaluation, including oculomotor testing, to provide a more thorough assessment of their learning-related difficulties. Full article