Search Results (160)

Grey models have attracted considerable attention as a time series forecasting tool in recent years. Nevertheless, the linear characteristics of the differential equations on which traditional grey models rely frequently result in inadequate predictive accuracy and applicability when addressing intricate nonlinear systems. This study introduces a conformable fractional order unbiased kernel-regularized nonhomogeneous grey model (CFUKRNGM) based on statistical learning theory to address these limitations. The proposed model initially uses a conformable fractional-order accumulation operator to derive distribution information from historical data. A novel regularization problem is then formulated, thereby eliminating the bias term from the kernel-regularized nonhomogeneous grey model (KRNGM). The parameter estimation of the CFUKRNGM model requires solving a linear equation with a lower order than the KRNGM model, and is automatically calibrated through the Bayesian optimization algorithm. Experimental results show that the CFUKRNGM model achieves superior prediction accuracy and greater generalization performance compared to both the KRNGM and traditional grey models. Full article

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space ($2^{383}$), exceptional key sensitivity, extremely low ciphertext pixel correlations (<0.002), excellent ciphertext entropy values (>7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of $99.6096\%$ and $33.4638\%$, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services. Full article

Accurate prediction of natural gas production is of great significance for optimizing development strategies, simplifying production management, and promoting decision-making. This paper utilizes partial differentiation to effectively capture the spatiotemporal characteristics of natural gas data and the advantages of grey prediction models. By introducing the fractional damping accumulation operator, a new fractional order partial grey prediction model is established. The new model utilizes partial capture of details and features in the data, improves model accuracy through fractional order accumulation, and extends the metadata of the classic grey prediction model from time series to matrix series, effectively compensating for the phenomenon of inaccurate results caused by data fluctuations in the model. Meanwhile, the principle of data accumulation is effectively expressed in matrix form, and the least squares method is used to estimate the parameters of the model. The time response equation of the model is obtained through multiplication transformation, and the modelling steps are elaborated in detail. Finally, the new model is applied to the prediction of natural gas production in Qinghai Province, China, selecting energy production related to natural gas production, including raw coal production, oil production, and electricity generation, as relevant variables. To verify the effectiveness of the new model, we started by selecting the number of relevant variables, divided them into three categories for analysis based on the number of relevant variables, and compared them with five other grey prediction models. The results showed that in the seven simulation experiments of the three types of experiments, the average relative error of the new model was less than 2%, indicating that the new model has strong stability. When selecting the other three types of energy production as related variables, the best effect was achieved with an average relative error of 0.3821%, and the natural gas production for the next nine months was successfully predicted. Full article

Water pollution from industrial and domestic sewage demands the accurate modeling of wastewater treatment processes. While the Lawrence–McCarty model is widely used for activated sludge systems, its integer-order formulation cannot fully capture the fractal characteristics of microbial aggregation. This study proposed a fractal Lawrence–McCarty model (FLMM) by incorporating local fractional derivatives (α = ln2/ln3) to describe microbial growth dynamics on Cantor sets. Theoretical analysis reveals that the FLMM exhibits Mittag-Leffler-type solutions, which naturally generate step-wise growth curves—consistent with the phased behavior (lag, rapid growth, and stabilization) observed in real sludge systems. Compared with classical models, the FLMM’s fractional-order structure provides a more flexible framework to represent memory effects and spatial heterogeneity in microbial communities. These advances establish a mathematical foundation for future experimental validation and suggest potential improvements in predicting nonlinear biomass accumulation patterns. Full article

In order to analyze the explosion risk of the engine room, this paper uses CFD software to simulate the LNG leakage process in the engine room of the ship, and uses the combustible gas cloud obtained from the leakage simulation to simulate the explosion, analyzing its combustion and explosion dynamics. On the basis of previous studies, this paper studies the coupling of leakage and explosion simulation to ensure that it conforms to the real situation. At the same time, taking explosion overpressure, explosion temperature, and the mass fraction of combustion products as the breakthrough point, this paper studies the harm of explosion to human body and the influence of ignition source location on the propagation characteristics of LNG explosion shock wave in the engine room, and discusses the influence of obstacles on gas diffusion and accumulation. The results show that the LNG leakage reaches the maximum concentration in the injection direction, and the obstacles in the cabin have a significant effect on the diffusion and accumulation of gas. In the explosion simulation based on the leakage results, it can be determined that the shape of the pressure field generated by the explosion is irregular, and the pressure field at the obstacle side has obvious accumulation. Finally, in order to reduce the explosion hazard, the collaborative strategy of modular layout, directional ventilation, and gas detection is proposed, which provides ideas for the explosion-proof design of the cabin. Full article

This study focuses on optimizing the thermal performance of hydrogen turbine blades through a sensitivity analysis using generalized fractional calculus. The approach is designed to capture the transient temperature dynamics and optimize thermal profiles by analyzing the influence of a fractional-order parameter on the system’s behavior. The model was implemented in Python, using Monte Carlo simulations to evaluate the impact of the parameter on the temperature evolution in different thermal regimes. Three distinct regions were identified: the Quasi-Uniform Region (where fractional effects are negligible), the Sub-Classical Region (characterized by delayed thermal behavior), and the Super-Classical Region (exhibiting enhanced heat accumulation). Regression analyses reveal quadratic and cubic dependencies of blade temperature on the fractional-order parameter, confirming the robustness of the model with R² values greater than 0.96. The study highlights the potential of using fractional calculus to optimize the thermal response of turbine blades, helping to identify the most suitable parameters for faster stabilization and efficient heat management in hydrogen turbines. Furthermore, it was found that by adjusting the fractional-order parameter, the system can be optimized to reach equilibrium more rapidly while achieving higher temperatures. Importantly, the equilibrium is not altered but rather accelerated based on the chosen parameter, ensuring a more efficient thermal stabilization process. Full article

Background: This study addresses the challenge of predicting data sequences characterized by a mix of partial linearity and partial nonlinearity. Traditional forecasting models often struggle to accurately capture the complex patterns of change within the data. Methods: To this end, this study introduces a novel polynomial-driven discrete grey power model (PFDPGM(1,1)) that includes time perturbation parameters, enabling a flexible representation of complex variation patterns in the data. The model aims to determine the accumulation order, nonlinear power exponent, time perturbation parameter, and polynomial degree to minimize the fitting error under various criteria. The estimation of unknown parameters is carried out by leveraging a hybrid optimization algorithm, which integrates Particle Swarm Optimization (PSO) and the Grey Wolf Optimization (GWO) algorithm. Results: To validate the effectiveness of the proposed model, the annual total renewable energy consumption in the BRICS countries is used as a case study. The results demonstrate that the newly constructed polynomial-driven discrete grey power model can adaptively fit and accurately predict data series with diverse trend change characteristics. Conclusions: This study has achieved a significant breakthrough by successfully developing a new forecasting model. This model is capable of handling data sequences with mixed trends effectively. As a result, it provides a new tool for predicting complex data change patterns. Full article

Influenced by the hydrogeological structure and other factors, the change in groundwater depth shows seasonal fluctuation characteristics. Human activities have disrupted the long-term stable pattern of groundwater change, which makes the short-term prediction of groundwater depth important. To cope with the emergence of short-term groundwater prediction scenarios, for the first time, a discrete grey seasonal model with fractional order accumulation is proposed in this paper (FDGSM(1,1)). First, the DGM(1,1) model, which has a relative advantage over fluctuating data, was chosen as the basis for the transformation of the proposed model. Then, the fractional order accumulation operator is used to reduce the seasonal fluctuations in the data series. Finally, grey seasonal variables are introduced to construct the time response function. The proposed model has the basic properties of the traditional grey forecasting model, which is proven to be stable and seasonal. Additionally, the prediction performance of the proposed model is verified in a real scenario of Handan groundwater. This paper expands the seasonal prediction field of the grey prediction model, enriches the research system of the grey system theory and fractional order, and has a positive influence on the short-term prediction of groundwater depth. Full article

Increased stemness of cancer cells exacerbates radioresistance, thereby greatly limiting the efficacy of radiotherapy. In order to study the changes in cancer cell stemness during radiotherapy, we established a radioresistance model of human non-small cell lung cancer A549 cells and obtained A549 radioresistant cells (A549-RR). We sampled the cells at different time points during the modeling process and investigated the heterogeneity of each group of cells using single-cell sequencing. Cells in the early stages of fractionated irradiation were found to be significantly up-regulated in stemness, and a subpopulation of cells producing this response was screened and referred to as “radiation-induced stemness-responsive cancer cells”. They were undergoing stemness response, energy metabolism reprogramming, and progressively differentiating into cells with more diverse and malignant phenotypes in order to attenuate the killing effect of radiation. Furthermore, we demonstrated that such responses might be driven by the activation of the EGFR-Hippo signaling pathway axis, which also plays a crucial role in the development of radioresistance. Our study reveals the dynamic evolution of cell subpopulation in cancer cells during fractionated radiotherapy; the early stage of irradiation can determine the destiny of the radiation-induced stemness-responsive cancer cells. The activation of stemness-like phenotypes during the development of radioresistance is not the result of dose accumulation but occurs during the early stage of radiotherapy with relatively low-dose irradiation. The degree of the radiation-induced stemness response of cancer cells mediated by the EGFR-Hippo signaling pathway might be a potential predictor of the efficacy of radiotherapy and the development of radioresistance. Full article

Motorcycles are widely used vehicles in Indonesia, not only as private vehicles but also for public transportation. Currently, there are many applications that help customers to use motorbikes as public transportation and are known as “online ojek” applications. Although there have been many online ojek applications used by the public, there is no online ojek application specifically for women. This study uses the conjoint method to determine the attributes of female consumer preferences for online ojek applications so that further studies the result of this study as a reference for developing female online ojek applications. With a sample size of 130 respondents, the combination of attributes is formed using fractional factorial design. This study produces eight attributes and levels that are most desired by consumers: (1) colourless, 3D supporting icons with, (2) a primary application colour of pink, (3) button shapes with blunt rectangles, (4) bold text for the level selected in the thick and thin text design, (5) application menu containing homepage, promo, order, chat, profile, thick and thin text, (6) Indonesian application language, (7) payment menu containing accumulated prices and accumulated minutes and (8) 3D and colourful icons. Full article

Using the data of radon accumulation in a chamber with excess volume at one of the points of the Kamchatka subsurface gas-monitoring network, the change in radon flux density due to seismic waves and post-seismic relaxation of the medium is shown. A linear fractional equation is considered to be a model equation. The change of radon-transport intensity due to changes in the state of the geo-environment is described by a fractional Gerasimov–Caputo derivative of constant order. Presumably, the order of the fractional derivative is related to the radon-transport intensity in the geosphere. Using the Levenberg–Marquardt method, the optimal values of the model parameters were determined based on experimental data: air exchange coefficient and order of fractional derivative, which allowed the solving of the problems of radon flux density determination. Data in the temporal neighborhood of a strong earthquake with $M_w=7.0$, which occurred in the northern part of Avacha Bay on 17 August 2024, were used. As a result of the modeling, it is shown that the strong seismic impact and subsequent processes led to changes in the radon flux in the accumulation chamber. The obtained model curves agree well with the real data, and the obtained estimates of radon flux density agree with the theory. Full article

The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. Fractional mathematical models also take into account the dependence of the rate of accumulation on capital productivity and the influx of external investment and new technological solutions. The effects of heredity lead to a delayed effect of the response of the system in question to the impact. The property of heredity in mathematical models is taken into account using fractional derivatives of constant and variable orders in the sense of Gerasimov–Caputo. The fractional mathematical models of S. V. Dubovsky are further studied numerically using the Adams–Bashforth–Moulton algorithm. Using a numerical algorithm, oscillograms and phase trajectories were constructed for various values and model parameters. It is shown that the fractional mathematical models of S. V. Dubovsky may have limit cycles, which are not always stable. Full article

In order to comprehensively understand the content, source, speciation characteristics, and risk of heavy metals in cultivated soil of Pingshui Village, Zhaoping County, Hezhou City, this study conducted measurements on the total amounts of Cr, Ni, Cu, Zn, As, Cd, Pb, and Hg in 34 soil samples within the study area. Correlation analysis and principal component analysis were employed to investigate their sources. An improved BCR sequential extraction procedure was utilized to analyze the occurrence forms of eight heavy metals in soil samples. Ecological risks were evaluated using the geo-accumulation index (I_geo), potential ecological risk index (RI), and risk assessment code (RAC). The findings revealed that: (1) The soil heavy metals in the study area exhibited varying degrees of enrichment, primarily attributed to anthropogenic activities. (2) There was no significant difference in the speciation characteristics of the eight heavy metals in the soil of each sampling site in the study area, and the main components were all residual fraction, and the mild acid-soluble fraction of Cd and Zn accounted for a relatively high proportion in individual sampling sites, which should be paid attention to. (3) Through the results of three risk assessment methods, it is concluded that the heavy metal pollution of soil in the study area is serious, and continuous attention should be paid to the corresponding pollution prevention measures. Full article

Soil contamination by many kinds of anthropogenic operations, such as industrial and mining activities, results in the accumulation of various heavy metal contaminants in the environment. Cadmium (Cd) and lead (Pb) are commonly found heavy metals in the Mahad Adahab mining area in Saudi Arabia. In this study, natural and modified zeolite sediments were fractioned by size to nano- and macrosizes and were applied to stabilize Cd and Pb from contaminated mining soil. Among the tested adsorbents, zeolite sediment in the nanosize that was modified by layered double hydroxides (LDH-N) showed the highest sorption and removal efficiency (>98%) for Cd and Pb, followed by nanosized natural zeolite (NZ-N) and HCl-modified nanosized natural zeolite sediment (HCl-N), which removed >90% Cd and Pb from contaminated soil. A pH of 7 was found to be optimal for Cd and Pb sorption, and the kinetics study revealed that first-order and pseudo-second-order kinetic models best fitted the experimental data (R² = 0.94–0.98) for Cd and Pb sorption by the tested sediments. An incubation period of 16 weeks revealed that LDH-N, HCl-N, and NZ-N reduced the ammonium acetate extractable fraction of Cd by 89.26, 83.70, and 80.54% and Pb by 86.19, 81.42, and 77.98%, respectively. Electrostatic interaction and ion exchange were found to be the principal mechanisms for Cd and Pb sorption. The findings of this study indicate that the utilization of modified zeolite sediment in the nanosize fraction (LDH-N, HCl-N, and NZ-N) could be an effective and feasible strategy in stabilizing heavy metals and mitigating their toxicity in contaminated mining soil. Full article

The trimodal grain-structured (TGS) carbon nanotube-reinforced aluminum matrix composites (CNT/Al) exhibit better strength–ductility synergy compared to bimodal grain-structured (BGS) composites. The addition of fine grain (FG) to the TGS composites effectively facilitates strain hardening and reduces strain/stress concentrations. In order to address the strain incompatibility in TGS composites, a significant accumulation of geometrically necessary dislocations (GNDs) occurs at the hetero-zone boundaries. This accumulation serves as the key factor in generating additional strengthening and work hardening. By utilizing a multi-mechanism strain gradient model, a quantitative analysis of the contributions made by Hall–Petch, Taylor, and back stress strengthening was conducted. Furthermore, effects of each domain volume fraction on the GND density at the boundaries between heterogeneous domains were carefully and extensively investigated and compared. It is found that the strengthening effect of back stress significantly surpasses that of the Hall–Petch and Taylor strengthening accounting. Compared to BGS composites, the TGS composites are more effective in facilitating strain hardening and reducing strain/stress concentrations, which may lead to a better balance between strength and ductility. Full article