Search Results (871)

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 $\mathsf{\lambda }=0$. 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

Water resources are strategic resources that support regional economic social development and maintain the health and stability of ecosystems. This study revealed the evolution of the coordinated development of China’s water resources–economic society–ecological environment system based on the coordination degree mode. The research was conducted by integrating machine learning with traditional mathematical methods; by setting up the status quo development scenario, water resources priority scenario, economic society priority scenario, ecological environment priority scenario and balanced development scenario; and by using the Holt exponential smoothing–feedforward neural network prediction model, the coordinated development trends under different scenarios were predicted. The results showed that, analyzed from the perspective of the coordinated evolution type of the dual systems, the dominant development system during the study period gradually transformed from water resources–economic society to water resources–ecological environment. For the coordinated development of the complex system, the coordination degree showed “stepped leap—resilient fluctuation (from 0.7242 to 0.8238)”, and “better in the southeast than in the northwest, with significant advantages in the coast”. The most significant increase in the coordination degrees were observed in the balanced development scenario and economic society priority scenarios, where it increased by an average of around 5%, confirming the effective contribution of stable economic and social development to the level of coordination. This study provides theoretical support and practical guidance for regional water resources management. Full article

This study presents the development of a software solution for processing, analyzing, and visualizing sensor data collected by an educational mobile robot. The focus is on statistical analysis and identifying correlations between diverse datasets. The research utilized the PlatypOUs mobile robot platform, equipped with odometry and inertial measurement units (IMUs), to gather comprehensive motion data. To enhance the reliability and interpretability of the data, advanced data processing techniques—such as moving averages, correlation analysis, and exponential smoothing—were employed. Python-based tools, including Matplotlib and Visual Studio Code, were used for data visualization and analysis. The analysis provided key insights into the robot’s motion dynamics; specifically, its stability during linear movements and variability during turns. By applying moving average filtering and exponential smoothing, noise in the sensor data was significantly reduced, enabling clearer identification of motion patterns. Correlation analysis revealed meaningful relationships between velocity and acceleration during various motion states. These findings underscore the value of advanced data processing techniques in improving the performance and reliability of educational mobile robots. The insights gained in this pilot project contribute to the optimization of navigation algorithms and motion control systems, enhancing the robot’s future potential in STEM education applications. Full article

The stability of hybrid stochastic differential equations (SDEs in short) depends on multiple factors, such as the structures and parameters of subsystems, switching rules, delay, etc. Regarding stability analysis for hybrid stochastic systems incorporating subsystems with diverse structures, existing research results require the system to possess either Markovian properties or finite memory characteristics. However, the stability problem remains unresolved for hybrid stochastic differential equations with infinite memory (hybrid IMSDEs in short), as no systematic theoretical framework currently exists for such systems. To bridge this gap, this paper develops a rigorous stability analysis for a class of hybrid IMSDEs by introducing a suitably chosen phase space and leveraging the theory of fading memory spaces. We establish sufficient conditions for exponential stability, extending the existing results to systems with unbounded memory effects. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria. Full article

The road construction sector urgently requires environmentally friendly, low-carbon, and high-performance base materials. Traditional materials exhibit issues of high energy consumption and carbon emissions, making it difficult for them to align with sustainable development requirements. While slag- and fly ash-based geopolymers demonstrate promising application potential in civil engineering, research on their application in road-stabilized soils remains insufficient. To address the high energy consumption and carbon emissions associated with conventional road base materials and to fill this research gap, this study investigated the utilization of industrial solid wastes through slag-based geopolymer and fly ash as stabilizers, systematically evaluating the pavement performance of two distinct soil types. Unconfined compressive strength tests and freeze–thaw cycling tests were conducted to elucidate the effects of stabilizer dosage, fly ash co-stabilization, and compaction degree on mechanical properties. The results demonstrated that the compressive strength of both stabilized soils increased significantly with higher slag-based geopolymer content, achieving peak values of 5.2 MPa (soil sample 1) and 4.5 MPa (soil sample 2), representing a 30% improvement over cement-stabilized soils with identical mix proportions. Fly ash co-stabilization exhibited more pronounced reinforcement effects on soil sample 2. At a 98% compaction degree, soil sample 1 maintained a stable 50% strength enhancement, whereas soil sample 2 displayed a dose-dependent exponential strength increase. Freeze–thaw resistance tests revealed the superior performance of soil sample 1, showing a loss of compressive strength (BDR) of 78% with 8% geopolymer stabilization alone, which improved to 90% after fly ash co-stabilization. For soil sample 2, the BDR increased from 64% to 80% through composite stabilization. This study confirms that slag/fly ash-based geopolymer-stabilized soils not only meet the strength requirements for heavy-traffic subbases and light-traffic base courses, but also demonstrates its great potential as a low-carbon and environmentally friendly material to replace traditional road base materials. Full article

Hydraulic excavators operate in harsh environments where direct measurement of actuator chamber pressures and boom displacement is often unreliable or infeasible. This study presents a novel control strategy that estimates actuator chamber pressures from work port pressures using differential equations, eliminating the need for direct pressure or position sensors. A fuzzy logic-based proportional–derivative (PD) controller is developed to mitigate boom oscillations, particularly under high-inertia load conditions and variable operator inputs. The controller dynamically adjusts gains through fuzzy logic-based gain scheduling, enhancing adaptability across a wide range of operating conditions. The proposed method addresses the limitations of classical PID controllers, which struggle with the nonlinearities, parameter uncertainties, and instability introduced by counterbalance valves and pressure-compensated proportional valves. Experimental data is used to design fuzzy rules and membership functions, ensuring robust performance. Simulation and full-scale experimental validation demonstrate that the fuzzy PD controller significantly reduces pressure overshoot (by 23% during extension and 32% during retraction) and decreases settling time (by 31.23% and 28%, respectively) compared to conventional systems. Frequency-domain stability analysis confirms exponential stability and improved damping characteristics. The proposed control scheme enhances system reliability and safety, making it ideal for excavators operating in remote or rugged terrains where conventional sensor-based systems may fail. This approach is generalizable and does not require modifications to the existing hydraulic circuit, offering a practical and scalable solution for modern hydraulic machinery. Full article

The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness of solutions with the defined conditions using integral equations. On top of that, an auxiliary result is established, outlining the relationship between the unknown function values in the deviation argument and the time parameter. The stability analysis is conducted using the Lyapunov–Razumikhin method, adapted for differential equations with a piecewise constant argument of the generalized type. The trivial equilibrium’s stability is examined, and the stability of the positive equilibrium is assessed by transforming it into a trivial form. Finally, sufficient conditions for the uniform asymptotic stability of both the trivial and positive equilibria are established. Full article

The progressive proliferation of sensor deployment in distribution networks (DNs), propelled by the dual drivers of power automation and ubiquitous IoT infrastructure development, has precipitated exponential growth in real-time data generated by multisource heterogeneous (MSH) sensors within multilayer grid architectures. This phenomenon presents dual implications: large-scale datasets offer an enhanced foundation for reliability assessment and dispatch planning in DNs; the dramatic escalation in data volume imposes demands on the computational precision and response speed of traditional evaluation approaches. The identification of critical influencing factors under extreme operating conditions, coupled with dynamic assessment and prediction of DN reliability through MSH data approaches, has emerged as a pressing challenge to address. Through a brief analysis of existing technologies and algorithms, this article reviews the technological development of MSH data analysis in DNs. By integrating the stability advantages of conventional approaches in practice with the computational adaptability of artificial intelligence, this article focuses on discussing key approaches for MSH data processing and assessment. Based on the characteristics of DN data, e.g., diverse sources, heterogeneous structures, and complex correlations, this article proposes several practical future directions. It is expected to provide insights for practitioners in power systems and sensor data processing that offer technical inspirations for intelligent, reliable, and stable next-generation DN construction. Full article

Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s² flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article

In cold regions, the rock mass of open-pit mine slopes is continuously exposed to freeze–thaw (FT) environments, during which the fracture structures and their infilling materials undergo significant degradation, severely affecting slope stability and the assessment of service life. Conventional laboratory FT tests are typically based on uniform temperature settings, which fail to reflect the actual thermal variations at different burial depths, thereby limiting the accuracy of mechanical parameter acquisition. Taking the Wushan open-pit mine as the engineering background, this study establishes a temperature–depth relationship, defines multiple thermal intervals, and conducts direct shear tests on structural plane filling materials under various FT conditions to characterize the evolution of cohesion and internal friction angle. Results from rock mass testing and numerical simulation demonstrate that shear strength parameters exhibit an exponential decline with increasing FT cycles and decreasing burial depth, with the filling material playing a dominant role in the initial stage of degradation. Furthermore, a two-dimensional fracture network model of the rock mass was constructed, and the representative elementary volume (REV) was determined through the evolution of equivalent plastic strain. Based on this, spatial assignment of slope strength was performed, followed by stability analysis. Based on regression fitting using 0–25 FT cycles, regression model predictions indicate that when the number of FT cycles exceeds 42, the slope safety factor drops below 1.0, entering a critical instability state. This research successfully establishes a spatial field of mechanical parameters and evaluates slope stability, providing a theoretical foundation and parameter support for the long-term service evaluation and stability assessment of cold-region open-pit mine slopes. Full article

Owing to its high energy efficiency, regenerative capability, and fast dynamic response, the Electromagnetic Energy-Feeding Shock Absorber has found widespread application in automotive suspension control systems. To further improve thrust control precision, this study presents a sliding mode thrust controller designed using an improved Gray Wolf Optimization algorithm. Firstly, an improved exponential reaching law is adopted, where a saturation function replaces the traditional sign function to enhance system tracking accuracy and stability. Meanwhile, a position update strategy from the particle swarm optimization (PSO) algorithm is integrated into the gray wolf optimizer (GWO) to improve the global search ability and the balance of local exploitation. Secondly, the improved GWO is combined with sliding mode control to achieve online optimization of controller parameters, ensuring system robustness while suppressing chattering. Finally, comparative analyses and simulation validations are conducted to verify the effectiveness of the proposed controller. Simulation results show that, under step input conditions, the improved GWO reduces the rise time from 0.0034 s to 0.002 s and the steady-state error from 0.4 N to 0.12 N. Under sinusoidal input, the average error is reduced from 0.26 N to 0.12 N. Under noise disturbance, the average deviation is reduced from 2.77 N to 2.14 N. These results demonstrate that the improved GWO not only provides excellent trajectory tracking and control accuracy but also exhibits strong robustness under varying operating conditions and random white noise disturbances. Full article

This paper introduces and analyzes a novel fractional-order Ananthakrishna model. The stability of its equilibrium points is first investigated using fractional-order stability criteria, particularly in regions where the corresponding integer-order model exhibits instability. A linear finite difference scheme is then developed, incorporating an accelerated L1 method for the fractional derivative. This enables a detailed exploration of the model’s dynamic behavior in both the time domain and phase plane. Numerical simulations, including Lyapunov exponents, bifurcation diagrams, phase and time diagrams, demonstrate that the fractional model exhibits stable and periodic behaviors across various fractional orders. Notably, as the fractional order approaches a critical threshold, the time required to reach stability increases significantly, highlighting complex stability-transition dynamics. The computational efficiency of the proposed scheme is also validated, showing linear CPU time scaling with respect to the number of time steps, compared to the nearly quadratic growth of the classical L1 and Grünwald-Letnikow schemes, making it more suitable for long-term simulations of complex fractional-order models. Finally, four types of stress-time curves are simulated based on the fractional Ananthakrishna model, corresponding to both stable and unstable domains, effectively capturing and interpreting experimentally observed repeated yielding phenomena. Full article

The demand for multimedia traffic over the Internet is exponentially growing. HTTP adaptive streaming (HAS) is the leading video delivery system that delivers high-quality video to the end user. The adaptive bitrate (ABR) algorithms running on the HTTP client select the highest feasible video quality by adjusting the quality according to the fluctuating network conditions. Recently, low-latency ABR algorithms have been introduced to reduce the end-to-end latency commonly experienced in HAS. However, a comprehensive study of the low-latency algorithms remains limited. This paper investigates the effectiveness of low-latency streaming algorithms in maintaining a high quality of experience (QoE) while minimizing playback delay. We evaluate these algorithms in the context of both Dynamic Adaptive Streaming over HTTP (DASH) and the Common Media Application Format (CMAF), with a particular focus on the impact of chunked encoding and transfer mechanisms on the QoE. We perform both objective as well as subjective evaluations of low-latency algorithms and compare their performance with traditional DASH-based ABR algorithms across multiple QoE metrics, various network conditions, and diverse content types. The results demonstrate that low-latency algorithms consistently deliver high video quality across various content types and network conditions, whereas the performance of the traditional adaptive bitrate (ABR) algorithms exhibit performance variability under fluctuating network conditions and diverse content characteristics. Although traditional ABR algorithms download higher-quality segments in stable network environments, their effectiveness significantly declines under unstable conditions. Furthermore, the low-latency algorithms maintained high user experience regardless of segment duration. In contrast, the performance of traditional algorithms varied significantly with changes in segment duration. In summary, the results underscore that no single algorithm consistently achieves optimal performance across all experimental conditions. Performance varies depending on network stability, content characteristics, and segment duration, highlighting the need for adaptive strategies that can dynamically respond to varying streaming environments. Full article

The capillary force driving the water penetration process in the coal pore network is the key factor affecting the effect of coal seam water injection. The resistivity method can be used to determine the migration characteristics of water in coal. In order to study the relationship between the resistivity of gas-bearing coal and the migration of water in the process of imbibition, the self-generated imbibition tests of coal under different external water conditions were carried out by using the self-developed gas-bearing coal imbibition experimental platform and the dynamic response characteristics of coal resistivity with external water were obtained. The results show that the water injected into the coal body migrates from bottom to top under the driving of capillary force, and the resistivity of the wetted coal body shows a sudden decline, slow decline, and gradually stable stage change. Through the slice drying method, it is found that the moisture in the coal body is almost uniform after imbibition, and the resistivity method can be used to accurately and quantitatively characterize the moisture content of the coal body. In the axial direction, as water infiltrates layer by layer, the sudden change time of resistivity is delayed with the deepening of the layer. The resistivity of each layer first drops sharply then slows down and tends to stabilize. The stable value of resistivity increases gradually with the depth of the layer. In the radial direction, within the same plane, water first migrates to the centre of the coal body and then begins to spread outwards. The average mutation time and stable value of coal resistivity during spontaneous imbibition decrease with increasing water content. When the water content reaches 10%, the stable value of resistivity tends to be constant, and the relationship between the stable value of coal resistivity and water content conforms to an exponential function. Full article

Coastal marine soft clays subjected to long-term storm wave loading often exhibit inclined initial principal stress orientation (α₀) and subsequent cyclic principal stress rotation (PSR). These stress states critically influence soil mechanical behavior and failure mechanisms, threatening offshore structural stability. This study employs hollow cylinder apparatus testing to investigate the undrained cyclic loading behavior of reconstituted soft clay under controlled α₀ and PSR conditions, simulating storm wave-induced stress paths. Results demonstrate that α₀ governs permanent pore pressure and vertical strain accumulation with distinct mechanisms, e.g., a tension-dominated response with gradual pore pressure rise at α₀ < 45° transitions to a compression-driven rapid strain accumulation at α₀ > 45°. Rotational loading with PSR significantly intensifies permanent strain accumulation and stiffness degradation rates, exacerbating soil’s anisotropic behavior. Furthermore, the stiffness degradation index tends to uniquely correlate with the permanent axial or shear strain, which can be quantified by an exponential relationship that is independent of α₀ and PSR, providing a unified framework for normalizing stiffness evolution across diverse loading paths. These findings advance the understanding of storm wave-induced degradation behavior of soft clay and establish predictive tools for optimizing marine foundation design under cyclic loading. Full article