Search Results (128)

This paper is dedicated to the investigation of new generalizations of the classical Gronwall–Bellman–Bihari integral inequalities, which are fundamental tools in the qualitative and quantitative analysis of differential, integral, and integro-differential equations. We establish two primary, novel theorems. The first theorem presents a significant generalization for inequalities involving composite nonlinear functions and iterated integrals. This result provides an explicit bound for an unknown function $u(t)$ satisfying an inequality of the form $\mathsf{\Phi }(u(t))\le a(t)+{\int }_{t_0}^t f(s)\mathsf{\Psi }(u(s))ds+{\int }_{t_0}^t g(s)\mathsf{\Omega }({\int }_{t_0}^s h(\tau )K(u(\tau ))d\tau )ds$. The proof is achieved by defining a novel auxiliary function and applying a rigorous comparison principle. The second main theorem establishes a new bound for a class of fractional integral inequalities involving the Riemann–Liouville fractional integral operator ${\mathcal{I}}^{\alpha }$ and a non-constant coefficient function $b(t)$ in the form $u(t)\le a(t)+b(t){\mathcal{I}}^{\alpha }[\omega (u(s))]$. This result extends several recent findings in the field of fractional calculus. The mathematical derivations are detailed, and the assumptions on the involved functions are made explicit. To illustrate the utility and potency of our main results, we present two applications. The first application demonstrates how our first theorem can be used to establish uniqueness and boundedness for solutions to a complex class of nonlinear integro-differential equations. The second application utilizes our fractional inequality theorem to analyze the qualitative behavior (specifically, the boundedness of solutions) for a generalized class of fractional integral equations. These new inequalities provide a powerful analytical framework for studying complex dynamical systems that were not adequately covered by existing results. Full article

This study introduces and analyzes several new functionals defined on the interval $[0,1]$, which are associated with weighted integral inequalities for geometrically–arithmetically ($GA$) convex functions. Building upon the classical Hermite–Hadamard and Fejér inequalities, we define mappings such as $\mathcal{G}\left(u\right)$, ${\mathcal{H}}_y\left(u\right)$, ${\mathcal{K}}_y\left(u\right)$, $\mathcal{N}\left(u\right)$, $\mathcal{L}\left(u\right)$, ${\mathcal{L}}_y\left(u\right)$, and ${\mathcal{S}}_y\left(u\right)$, which incorporate a $GA$-convex function x and a non-negative, integrable weight function y that is symmetric about the geometric mean $\sqrt{s_1{s}_2}$. Under these conditions, we establish novel Fejér-type inequalities that connect these functionals. Furthermore, we investigate essential properties of these mappings, including their $GA$-convexity, monotonicity, and symmetry. The validity of our main results is demonstrated through detailed examples. The findings presented herein provide significant refinements and weighted generalizations of known results in the literature. Full article

Artificial Intelligence (AI) is increasingly framed as a driver of economic transformation, yet its capacity to alleviate poverty in the Global South remains contested. This article introduces the notion of AI Economics—the political economy of value creation, extraction, and redistribution in AI systems—to interrogate h ow innovation agendas intersect with structural inequalities. This article examines how Social Innovation (SI) systems, when coupled with decentralized Web3 technologies such as blockchain, Decentralized Autonomous Organizations (DAOs), and data cooperatives, may challenge data monopolies, redistribute economic gains, and support inclusive development. Drawing on Action Research (AR) conducted during the AI4SI International Summer School in Donostia-San Sebastián, this article compares two contrasting ecosystems: (i) the Established AI4SI Ecosystem, marked by centralized governance and uneven benefits, and (ii) the Decentralized Web3 Emerging Ecosystem, which promotes community-driven innovation, data sovereignty, and alternative economic models. Findings underscore AI’s dual economic role: while it can expand digital justice, service provision, and empowerment, it also risks reinforcing dependency and inequality where infrastructures and governance remain weak. This article concludes that embedding AI Economics in context-sensitive, decentralized social innovation systems—aligned with ethical governance and the SDGs—is essential for realizing AI’s promise of poverty alleviation in the Global South. Full article

In this study, we introduce and rigorously formalize the notion of (P, m)-superquadratic stochastic processes, representing a novel and far-reaching generalization of classical convex stochastic processes. By exploring their intrinsic structural characteristics, we establish advanced Jensen and Hermite–Hadamard ($\mathbb{H}.\mathbb{H}$)-type inequalities within the mean-square stochastic calculus framework. Furthermore, we extend these inequalities to their fractional counterparts via stochastic Riemann–Liouville ($\mathbb{RL}$) fractional integrals, thereby enriching the analytical machinery available for fractional stochastic analysis. The theoretical findings are comprehensively validated through graphical visualizations and detailed tabular illustrations, constructed from diverse numerical examples to highlight the behavior and accuracy of the proposed results. Beyond their theoretical depth, the developed framework is applied to information theory, where we introduce new classes of stochastic divergence measures. The proposed results significantly refine the approximation of stochastic and fractional stochastic differential equations governed by convex stochastic processes, thereby enhancing the precision, stability, and applicability of existing stochastic models. To ensure reproducibility and computational transparency, all graph-generation commands, numerical procedures, and execution times are provided, offering a complete and verifiable reference for future research in stochastic and fractional inequality theory. Full article

Despite extensive research on smartphone phubbing among youth, its manifestation among older adults remains overlooked in digital sustainability frameworks. This study challenges pathological framings by examining phubbing as potential compensation for structural constraints in China’s urban aging context. Adopting a theoretical thematic analysis approach, we interviewed 24 urban Chinese older adults (aged 60–75, daily smartphone use >4 h) from April to September 2024. Data underwent three-stage NVivo coding, distilling 156 initial codes into 19 thematic categories and five analytical dimensions through iterative refinement and member checks. Analysis revealed smartphone phubbing as structured compensation driven by push factors (empty-nest loneliness, mandatory retirement, epistemic devaluation) and pull factors (affordance-need matching). Cultural capital stratified outcomes: high-capital users attributed difficulties to ageist design while low-capital users internalized failures. Recursive feedback loops transformed use into dependency traps with health and financial consequences. Extending Push–Pull–Mooring theory, we developed a Digital Compensation Framework identifying epistemic inequality as a third-order digital divide. By reframing phubbing as a structural issue and advocating interventions addressing institutional foundations through universal design and platform responsibility, the framework illuminates pathways toward sustainable digital aging and directly advances UN Sustainable Development Goals for health (3), industry (9), equality (10) and partnership (17). Full article

This paper investigates the mean square exponential stability (MSES) and $H_{\infty }$ performance analysis of discrete networked control systems (NCSs) based on the FlexRay protocol (FRP) when confronted with randomly occurring cyber attacks (ROCAs). In order to deal with network congestion due to the limited bandwidth, the FRP is used to schedule the information exchange. Besides, a comprehensive attack model is built by simultaneously considering false data injection (FDI) attacks and denial-of-service (DoS) attacks. Then, a mode-dependent output feedback controller is designed on this basis. Furthermore, sufficient conditions for the MSES and $H_{\infty }$ performance of the considered system are derived under the mode-dependent Lyapunov function and average dwell time (ADT) constraints. Subsequently, the controller gains of two modes are determined by solving the recursive linear matrix inequalities (RLMIs) and the FRP-based MSES algorithm is also presented. The simulation verifies that the proposed algorithm maintains the system stability with good robustness and $H_{\infty }$ performance under ROCAs. Full article

Short sleep duration (≤6 h) is a public health concern linked to cardiometabolic disease and premature mortality. However, persistent disparities across sociodemographic, psychosocial, and structural domains remain underexplored in recent nationally representative samples. We analyzed 2022 Behavioral Risk Factor Surveillance System (BRFSS) data, including 228,463 adults (weighted N ≈ 122 million). Sleep duration was dichotomized as short (≤6 h) versus adequate (≥7 h). Complex samples logistic regression estimated associations between sociodemographic, psychosocial, behavioral, and structural determinants and short sleep, accounting for survey design. The weighted prevalence of short sleep was 33.2%. Non-Hispanic Black (AOR = 1.56, 95% CI: 1.46–1.65) and American Indian/Alaska Native adults (AOR = 1.46, 95% CI: 1.29–1.65) were disproportionately affected compared with non-Hispanic White adults. Psychosocial factors contributed strongly: life dissatisfaction, limited emotional support, and low social connectedness increased odds, whereas high connectedness was protective. Food insecurity and smoking were significant structural and behavioral risks, while binge drinking and urbanicity were not. One-third of U.S. adults report short sleep, with marked disparities across demographic, socioeconomic status, psychosocial stressors, and structural barriers. Findings highlight the multifactorial nature of sleep health inequities and the need for multilevel interventions addressing both individual behaviors and upstream determinants. Full article

Heating and cooling (H&C) account for nearly half of the EU’s energy consumption, with significant potential for decarbonization through renewable energy sources (RES) integrated in district heating and cooling (DHC) systems. This study evaluates the environmental and social impacts of RES-powered DHC solutions implemented in three European small-scale demo sites (Bucharest, Luleå, Córdoba) under the Horizon 2020 WEDISTRICT project. Using the Life Cycle Assessment (LCA) and Social Life Cycle Assessment (S-LCA) methodologies, the research compares baseline fossil-based energy scenarios with post-implementation renewable scenarios. Results reveal substantial greenhouse gas emission reductions (up to 67%) and positive environmental trade-offs, though increased mineral and metal resource use and site-specific impacts on water and land use highlight important sustainability challenges. Social assessments demonstrate improvements in gender parity, local employment, and occupational safety, yet reveal persistent issues in wage equity, union representation, and inclusion of vulnerable populations. The findings emphasize that while renewable DHC systems offer significant climate benefits, social sustainability requires tailored local strategies and robust governance to avoid exacerbating inequalities. This integrated environmental-social perspective underscores the need for holistic policies that balance technical innovation with equitable social outcomes to ensure truly sustainable energy transitions. Full article

The theory of integral inequalities has a wide range of applications in physics and numerical computation, and plays a fundamental role in mathematical analysis. The present study delves into the attractive domain of Hermite–Hadamard–Mercer (H–H–M)-type inequalities having a special emphasis on Wright’s general functions, referred to as Raina’s functions in the scientific literature. The main goal of our progressive study is to use Raina’s Fractional Integrals to derive two useful lemmas for second-differentiable functions. Using the derived lemmas, we proved a large number of fractional integral inequalities related to trapezoidal and midpoint-type inequalities where those that are twice differentiable in absolute values are convex. Some of these results also generalize findings from previous research. Next, we provide applications to error estimates for trapezoidal and midpoint quadrature formulas and to analytical evaluations involving modified Bessel functions of the first kind and q-digamma functions, and we show the validity of the proposed inequalities in numerical integration and analysis of special functions. Finally, the results are well-supported by numerous examples, including graphical representations and numerical tables, which collectively highlight their accuracy and computational significance. Full article

This study explores some new symmetric quantum inequalities that are based on Breckner’s convexity. By using these concepts, we propose new versions of Hermite–Hadamard (H-H) and Fejer-type inequalities. Additionally, we establish a new integral identity which helped us to derive a set of new quantum inequalities. Using the symmetric quantum identity, Breckner’s convexity, and several other classical inequalities, we develop blended bounds for a general quadrature scheme. To ensure the significance of this study, a few captivating applications are discussed. Full article

In this paper, the virtual model development and control for a BallBot Robotic System (BRS) are addressed. A virtual three-dimensional (3-D) EV3 BRS (EV3BRS) model is here developed through the Simscape^™ Multibody^™ environment from a BRS designed using the kit LEGO^® MINDSTORMS^® EV3. The mathematical model from the BRS is obtained through the Euler–Lagrange approach and used as the foundation to develop the EV3BRS Simscape^™ model. The electrical model for the motors is derived through Kirchhoff’s laws. To verify the dynamics of the EV3BRS Simscape^™ model, a Takagi–Sugeno Fuzzy Controller (TSFC) is designed using the Parallel Distributed Compensation (PDC) technique. Control gains are computed via Linear Matrix Inequalities (LMIs). To test the EV3BRS Simscape^™ model under disturbances, an input voltage anomaly is considered. So, adding an $H_{\infty }$ attenuation to the TSFC ensures that the EV3BRS Simscape^™ model faces these kind of anomalies. Simulation results confirm that the TSFC with $H_{\infty }$ attenuation improves the performance under anomalies at the input in contrast with the nominal TSFC, although this latter can maintain the body of the system near the upright position also. The dynamics from the EV3BRS Simscape^™ model here developed allow us to realize how the real system will behave. Full article

This paper proposes the expressions for the motor airgap torque harmonics induced by a cascaded H-bridge inverter operating with failed cells. These variable frequency drive systems (VFDs), are widely used in oil and gas applications, where a torsional vibration evaluation is a critical challenge for field engineers. This paper proposes mathematical expressions that are crucial for an accurate torsional analysis during the design stage of VFDs, as required by international standards such as API 617, API 672, etc. By accurately reconstructing the electromagnetic torque from the stator voltages and currents in the (αβ0) reference frame, the obtained expressions enable the precise prediction of the exact locations of torque harmonics induced by the inverter under various real-world operating conditions, without the need for installed torque sensors. The neutral-shifted and peak-reduction fault-tolerant control techniques are commonly adopted under faulty operation of these VFDs. However, their effects on the pulsating torques harmonics in machine air-gap remain uncovered. This paper fulfils this gap by conducting a detailed evaluation of spectral characteristics of these fault-tolerant methods. The theoretical analyses are supported by MATLAB/Simulink 2024 based offline simulation and Typhoon based virtual real-time simulation results performed on a (4.16 kV and 7 MW) vector-controlled induction motor fed by a 7-level cascaded H-bridge inverter. According to the theoretical analyses- and simulation results, the Neutral-shifted and Peak-reduction approaches rebalance the motor input line-to-line voltages in the event of an inverter’s failed cells but, in contrast to the normal mode the carrier, all the triplen harmonics are no longer suppressed in the differential voltage and current spectra due to inequal magnitudes in the phase voltages. These additional current harmonics induce extra airgap torque components that can excite the lowly damped eigenmodes of the mechanical shaft found in the oil and gas applications and shut down the power conversion system due torsional vibrations. 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

This study presents advanced control and energy management strategies for uncertain wind energy systems using a Takagi–Sugeno (T-S) fuzzy modeling framework. To address key challenges, such as system uncertainties, external disturbances, and input delays, the study integrates a fuzzy H∞ robust control approach with a neural network-based delay compensation mechanism. A fuzzy observer-based H∞ tracking controller is developed to enhance robustness and minimize the impact of disturbances. The stability conditions are rigorously derived using a quadratic Lyapunov function, H∞ performance criteria, and Young’s inequality and are expressed as Linear Matrix Inequalities (LMIs) for computational efficiency. In parallel, a neural network-based controller is employed to compensate for the input delays introduced by online learning processes. Furthermore, an energy management layer is incorporated to regulate the power flow and optimize energy utilization under varying operating conditions. The proposed framework effectively combines control and energy coordination to improve the systems’ performance. The simulation results confirm the effectiveness of the proposed strategies, demonstrating enhanced stability, robustness, delay tolerance, and energy efficiency in wind energy systems. Full article

Harmonic functions are renowned for their application in the analysis of minimal surfaces. These functions are also very important in applied mathematics. Any harmonic function in the open unit disk $\mathbb{U}=\left\{z\in \mathbb{C}:\left|z\right|<1\right\}$ can be written as a sum $f=h+\overline{g}$, where h and g are analytic functions in $\mathbb{U}$ and are called the analytic part and the co-analytic part of f, respectively. In this paper, the harmonic shear $f=h+\overline{g}\in S_{\mathcal{H}}$ and its rotation $f^{\mu }$ by $\mu \left(\mu \in \mathbb{C},\left|\mu \right|=1\right)$ are considered. Bounds are established for this rotation $f^{\mu }$, specific inequalities that define the Jacobian of $f^{\mu }$ are obtained, and the integral representation is determined. Full article