In this paper, a distributed–order Caputo fractional derivative is used to represent nonlinear heat wave propagation in rigid thermal conductors using a novel numerical approach. The suggested model takes into consideration memory effects that are a part of thermal wave transmission and captures non-Fourier heat conduction behavior. We use a fourth-order compact finite difference approach for spatial discretization to solve the governing nonlinear fractional partial differential equation, guaranteeing good accuracy with a small stencil. In order to handle the fractional–order integration over a continuous range with flexibility and enhanced stability, a weighted average non-standard finite difference method is employed for the temporal discretization of the distributed–order Caputo derivative. The created method’s accuracy, efficiency, and convergence are shown by numerical experiments. The findings demonstrate the model’s capacity to represent intricate thermal behaviors in rigid material by demonstrating the substantial influence of the distributed-order kernel on the propagation properties of thermal waves.
Intelligent home terminals serve as the key link between user personalized needs and the coordinated operation of home devices. Their performance directly affects the living experience, device energy efficiency, and response speed to user demands. Current control methods for intelligent home terminals face challenges such as insufficient collaborative processing of heterogeneous data sources and weak adaptability to dynamic scenarios, which limits precise control decisions in complex home environments. This study proposes an intelligent home terminal control method based on a Multi-sensor Data Fusion algorithm. It enhances the efficiency of integrating multiple data sources through the high-dimensional feature classification capability of Support Vector Machines and optimizes uncertain decision outputs using the probabilistic reasoning ability of Bayesian Networks, achieving high-precision dynamic control of intelligent home terminals. Test results show that the model achieves 98.15 % accuracy in environmental feature recognition in the training set and a control command response time of 38.51 ms. In the indicator tests, the accuracy of unstructured feature extraction reaches 98.72 %. These results demonstrate that the proposed model effectively addresses the insufficient multi-modal data fusion and weak adaptability in current intelligent home terminal control, providing a new pathway for the optimised design of intelligent home terminals.
Existing intelligent robots in vocational training lack the ability to perceive and adaptively adjust the trainees’ states in real time. Furthermore, existing lightweight models struggle to balance efficiency and accuracy, limiting their application in real-time interactive scenarios. Therefore, this study proposes an adaptive vocational training robot system based on a lightweight model and emotion perception. The system first constructs a classroom emotion dataset, then uses a residual network and a 16-layer visual geometry network to build a multimodal perception model. Feature fusion is enhanced through attention mechanisms and a feature pyramid network. Subsequently, depthwise separable convolution and pruning are used to achieve model lightweighting, ultimately integrating these elements to construct the adaptive vocational training robot system. Experimental findings demonstrate that when the data batch size increases to 32, the number of floating-point operations reaches 82.1 M. With a pruning rate of 70 %, the compression rate increases to 73.4 %. With a data volume of 8 k, the end-to-end latency only increases to 82 ms. At an illumination intensity of 500 lux, the highest attention assessment accuracy is 89.7 %. With 30 participants, the highest performance improvement rate reaches 34.8 %. The results show that the system has excellent response speed, robustness and teaching effectiveness, providing a feasible technical path and practical reference for adaptive technology in the field of vocational education.
This study proposes a self-similar transformation method to solve time-fractional partial differential equations (PDEs) in robotic systems. Unlike conventional models limited to ODEs, our approach captures memory effects and complex dynamics through fractional-order modeling. The reduced form allows analytical treatment while preserving physical behavior. We apply this method to robotic manipulation of acoustic waves, including energy focusing and suppression tasks. The results demonstrate improved prediction accuracy and control performance, offering a promising framework for advanced applications in soft and wave-based robotics.
In this paper, we discuss the existence of a unique solution and Ulam-Hyers-Mittag-Leffler (UHML) stability for a nonlinear Hammerstein-type psi-Hilfer delay differential equation of fractional order (psi-HFDDE) in the configuration of several variable time-dependent delays. Our study is based on fixed-point methodology. The results established in this work are novel and enhance the literature on the topic. We also present examples to illustrate the application of the obtained results. The findings of this paper provide new contributions to the qualitative theory of Hilfer fractional delay differential equations.
In this study, we investigate the application of the meshless collocation technique using radial basis functions (RBF) to approximate a class of linear and nonlinear fractional order delay-integro-differential equations with vanishing variable delays. Such equations, formulated within the framework of fractional calculus, are particularly useful for modeling processes with memory and hereditary characteristics, providing a more accurate representation of many physical and engineering phenomena than classical integer-order models. First, we prove the existence and uniqueness of solutions of the studied equation for both linear and nonlinear cases. Then, we develop an RBF interpolation combined with the Gauss-Legendre quadrature formula, enabling the proposed approach to solve the equations without relying on background approximation cells. The developed method is computationally efficient, stable, and requires low memory. Furthermore, the error analysis of this scheme is discussed. Several computational tests are presented to demonstrate the reliability and precision of the proposed technique for solving the considered equations. The obtained results are compared with analytical solutions, the moving least squares method, and other existing approaches to confirm the effectiveness and applicability of the proposed scheme.
The Klein-Fock-Gordon equation (KFGE) is a fundamental relativistic wave equation central to quantum mechanics and quantum field theory. It plays an important role in modeling particle dynamics during intense laser-plasma interactions. The nonautonomous KFGE (NAKFGE) was not considered in the literature. This may be argued to the presence of time-dependent parameters, as, in this case, the derivation of solutions is not straight forward. Here, the NAKFGE is studied for the first time. This study pursues two primary objectives, the derivation of exact self-similar solutions of the NAKFGE for a single wave structure, and the development of a new technique for multiple solutions employing the extended unified method (EUM). The exact analytical solutions obtained provide deeper insight into plasma wave dynamics and their relevance to fusion phenomena. In particular, the results reveal strong wave-fusion behavior when the nonlinearity index n lies within the interval 0 < n < 3. This fusion predominantly occurs in the positive spatial domain, indicating favorable conditions for effective energy confinement. Moreover, the estimated hydrogen-plasma temperature reaches approximately 1.5 & times; 10(8) K, exceeding the threshold required for thermonuclear fusion. Further, these results highlight the essential influence of the gain coefficient on both the plasma temperature and the resulting wave-fusion structures. The study also emphasizes the critical role of initial stability: surpassing certain diffusion-coefficient thresholds can drive the system toward instability. Indeed this work provides important theoretical framework for future experimental and numerical investigations aimed at achieving controlled thermonuclear fusion. The intricate interplay among wave characteristics, nonlinear effects, and stability emerges as a key factor in advancing our understanding of the fusion process.
In this work, we establish novel existence and uniqueness results for parabolic quasi-variational inequalities (PQVIs) by developing a structured four-phase numerical framework. The proposed methodology combines spatial discretization via finite element methods (FEM) with a semi-implicit time-stepping scheme to enhance stability and convergence. We construct a discrete iterative algorithm by linking the underlying variational system to a fixed-point formulation and further enrich it using a monotone iterative scheme inspired by Bensoussan's approach. To ensure mathematical rigor, we first present precise definitions and assumptions on the operators, coefficients, and source terms. Subsequently, the algorithm is fully developed and its consistency and stability are rigorously justified. A comprehensive convergence analysis is then provided, extending classical results to the FEM setting, and highlighting the impact of variational inconsistencies inherent to the discretization. Under strengthened regularity assumptions on the source term f, we derive refined error estimates in appropriate Sobolev norms, e.g., & Vert; u - u h & Vert; H 1 ( Omega ) <= C h alpha ${\Vert}u-{u}_{h}{{\Vert}}_{{H}<^>{1}\left({\Omega} ight)}\le C{h}<^>{\alpha }$ , where u and u h denote the continuous and discrete solutions, respectively. Our findings provide both theoretical validation and practical guidance for implementing FEM in challenging fractional, nonlocal, and impulse-control-related PQVIs.
Density Peak Clustering (DPC) is a widely used clustering method that automatically identifies cluster centers based on local density and distance metrics. However, DPC tends to converge to local optimal solutions when processing datasets with uneven density distributions. This paper proposes DPC-DIST, an improved algorithm that addresses this limitation through a geometric distribution coefficient delta. By incorporating spatial distribution characteristics into density calculations, DPC-DIST effectively prevents convergence to suboptimal solutions. Comprehensive experiments on six benchmark datasets (Wine, Iris, Seeds, Blobs, R15, R3) demonstrate that DPC-DIST consistently outperforms the original DPC, K-means++, and spectral clustering algorithms. Significant improvements were observed in high-dimensional data processing, with 9.3 % increase in Silhouette Coefficient and 47.7 % improvement in Calinski-Harabasz Score on the Wine dataset. The algorithm shows particular advantages in facility location optimization and logistics planning applications, demonstrating its practical value for real-world scenarios.
The explosive growth of Internet of Things (IoT)-driven imaging in medicine, city surveillance, and intelligent infrastructure requires secure, timely transportation of delicate visual information with salient information, like faces and diagnostically important medical areas. Standard block ciphers, including AES, are unable to consistently retain these attributes under burst errors, partial data corruption, or focused cropping. In this paper, we introduce a lightweight substitution–permutation network (SPN) oriented encryption paradigm purpose-built for salient information secrecy in resource-limited IoT applications. We integrate permutation-driven block shuffle by chaos, recurrent neural network (RNN)-guided nonlinear static S-box generation, and bit-parity scrambling at the bit level to improve confusion–diffusion properties. We demonstrate experimental results of NPCR > 99.60 %, UACI > 33.40 %, near-zero correlation, and satisfactory key sensitivity. The technique maintains integrity of the salient region even with 50 % pixel loss, with throughput acceptable for real-time applications. Compared with previous work on lightweight approaches, we provide improved salient feature retention and lower computational complexity, and thus an ideal solution to security-critical applications of IoT-driven imaging.
This research employs two analytical techniques, the modified Kudrynshov and the modified alternative G′G $\left(\frac{{G}^{\prime }}{G}\right)$ -expansion method, to investigate the soliton solutions of the well-known Zoomeron (Z) model, which arises in plasma physics, nonlinear optics, and fluid dynamics. This yields various soliton outcomes with distinct dynamic patterns, including bright solitons, localized waves, singular breather waves, kink and anti-kink patterns, and multi-breather waveforms. We attach three-dimensional, density, and two-dimensional curves to highlight the visual dynamics pattern of the outcomes. After that, we investigate equilibrium points in different scenarios to verify their stability. We also present phase portraits and various chaos assessment tools, such as return maps, Lyapunov exponents, strange attractors, and multistability, to confirm the presence of chaotic patterns in the proposed model. The results of this research will have significant implications for the future of advanced non-linear phenomena.
In the increasingly dominant consumer market of contemporary e-commerce, it has become urgent for enterprises to have a deeper and more comprehensive understanding of their e-commerce customers. A new method combining the K-means clustering algorithm with a backpropagation neural network has been proposed in the study. Specifically, customer data are first preprocessed through K-means clustering. Then, the initial weight distribution of the data is determined based on the clustering results to optimize the initial weight setting of the backpropagation neural network, thereby accelerating convergence during model training and effectively avoiding the problem of getting stuck in local optima. The results showed that the use of K-means clustering on customer information had a greater impact on the prediction ability of the algorithm model. The Geometric Means (G-means) and F1-values of the prediction model combining K-means clustering and backpropagation neural network were about 15 % and 31 % higher than those of the C4.5 decision tree algorithm, Support Vector Machine (SVM), and Logistic Regression algorithms, respectively. The area under the curve, accuracy, precision, and recall were 0.045, 0.037, 0.042, and 0.021 higher than those of backpropagation neural networks, respectively. The experimental results meet expectations, indicating that the proposed model is suitable for predicting customer churn in e-commerce.
This work presents the development of a two-species prey and predator model in the context of global warming. Studies indicate prey’s growth rate and predator anxiety are inversely correlated. Furthermore, evidence supports as global warming increases, prey’s carrying capacity may decline. Predators are thought to be able to work together to pursue prey. Furthermore, current thinking holds that the direction of the wind may affect how much prey the predator consumes. Scholars propose that when global warming increases, predator growth rates may decline. Additionally, experts argue that the intraspecies competition among predators, which is reliant on the density of the current prey, may result in a decline in the number of predators. It is widely accepted that the rate of global warming is constant. Furthermore, the prevailing view is that both predator and prey species may be involved in the rise in global warming. It is commonly understood that several industrial and ecological measures could reduce global warming. The model’s solution’s positivity and boundedness have been examined. Various equilibrium points are assessed, and the system’s stability is examined around these places. The Hopf bifurcation around the positive equilibrium point is investigated. Via numerical simulation and testing on a virtual data set, all theoretical results are experimentally validated.
The study proposes an anti-interference method based on Radio Frequency Identification (RFID) technology to solve the shortcomings of current wireless passive sensors on signal reception strength and anti-interference capability. The new method improves the signal recognition capability of RFID technology by introducing the blind equalization algorithm, and further enhances the security and anti-interference effect through frequency authentication technology. The results showed that the designed method significantly improved the anti-interference performance and transmission distance of the sensor signal, and had better stability and reliability than that of the traditional method. This designed method has significant practical significance in fields such as Industrial Internet of Things and smart cities. It can effectively improve the accuracy and reliability of sensor data, enhancing the efficiency and safety of the entire system, and laying a foundation for achieving more intelligent and efficient wireless communication systems and Internet of Things applications.
The paper illustrates traffic flow dynamics using partial differential equations derived from data using the Physics-Informed Information Criterion technique [1]. Thus, the aim is to explain the effect of various noise levels by varying the convection term and diffusion coefficients over time. First, we analyze the model using the Lie symmetry approach and also obtain an optimal system. Using these optimized systems, traffic flow densities are calculated to study the effect of noisy data on the results. In addition, the flow of traffic densities is obtained via a traveling wave. Kink-type graphical representations are obtained, which aid in traffic congestion prediction. By understanding and predicting traffic behavior under certain noise levels, this approach significantly contributes to traffic management strategy development.
Kuijpers’s study, published in Science under the title “Cavitation-induced reactions in high-pressure carbon dioxide,” explores the phenomenon of acoustic cavitation in high-pressure liquid CO 2 . However, an analysis of the study suggests that the vapor pressure within bubbles in high-pressure liquid CO 2 cannot remain constant or be balanced by static pressure, challenging the fundamental conditions required for acoustic cavitation. A critical prerequisite for cavitation is that the sound pressure must be proportional to the hydrostatic pressure, a condition that does not hold in Kuijpers’s experiments. This raises questions about the interpretation of the ultrasonic effects reported in the study, suggesting that they may not be caused by cavitation. The controversy surrounding acoustic cavitation in high-pressure CO 2 is of significant academic interest, as it has implications for fields such as chemical processing, materials science, and ultrasound-assisted reactions. While the physical properties of supercritical CO 2 closely resemble those of liquid CO 2 , experiments conducted with supercritical CO 2 indicate that metal corrosion and polymer formation can occur in the absence of cavitation. Moreover, computational simulations have further demonstrated the mechanical effects of ultrasound in both liquid and supercritical CO 2 , reinforcing the need for a more precise understanding of the mechanisms involved.
This study investigates the dynamics of a discrete-time epidemic model of COVID-19 formulated on the basis of the Lotka–Volterra framework. The positivity and boundedness of solutions are established to ensure biological feasibility. A stability analysis identifies equilibrium points and reveals critical bifurcations that influence disease transmission. Numerical simulations confirm the occurrence of flip and Neimark–Sacker bifurcations, leading to complex periodic and quasi-periodic oscillations. The analysis of Lyapunov exponents further highlights the transition from stable dynamics to chaotic behavior as key parameters vary. In addition, effective chaos-control strategies are explored to stabilize the system, thereby mitigating unpredictable epidemic oscillations and promoting reliable long-term disease dynamics. These findings underscore the importance of controlling epidemiological factors to prevent irregular epidemic waves and to maintain long-term stability in disease transmission.
University libraries are one of the important places to cultivate talents and conduct scientific research, but with the invasion of big data on the Internet, traditional library services cannot accurately understand readers’ needs, leading to a decline in library attendance. To solve this problem, the study proposes to combine multi-view K-mean clustering algorithm with reader behavior analysis to build a college library user portrait system to serve readers. When the enhanced K-mean clustering algorithm from the research was put to the test, the results showed that it performed better than the other two comparison algorithms, with accuracy and loss values of 97 % and 4.3 %, respectively. The user profile method that was suggested in the study was then empirically examined. The findings revealed that, when utilised with university students, the system was effective in raising the attendance rate of students by up to 75 %. In conclusion, it is clear that the method suggested in the study may accurately depict user profiles and offer readers good services, increasing the likelihood that readers will visit university libraries and lowering the waste of educational resources.
In this article, the complex structure of optical soliton solutions of the nonlinear Schrödinger–Bopp–Podolsky system is investigated using the enhanced modified extended tanh-expansion approach. It also analyzes the system’s stability and how it changes by performing a bifurcation analysis. This system holds special importance in nonlinear optics because it describes light-wave behavior when they interact with nonlinear materials. The enhanced modified extended tanh-expansion method serves as a strong analytical method to construct numerous innovative and diverse optical solitons including dark and bright and singular types. The obtained solutions help researchers understand all aspects that influence the nonlinear Schrödinger–Bopp–Podolsky system behavior while providing tools for simulating nonlinear optical processes. The potential for discovering new types of optical soliton solutions specific to the Schrödinger–Bopp–Podolsky system, which may differ from those found in other systems, remains untapped. While the current literature demonstrates the effectiveness of the enhanced modified extended tanh-method in various contexts, its application to the nonlinear Schrödinger–Bopp–Podolsky system could provide new insights and expand the understanding of soliton dynamics in modified nonlinear systems.This study is innovative because it is the first to apply the enhanced modified extended tanh-method to the nonlinear Schrödinger–Bopp–Podolsky system. This approach enables the construction of new soliton solutions and provides a deeper understanding of the nonlinear dynamics of the system. We employed Mathematica and MATLAB together to provide comprehensive, illustrative, and high-quality visualizations of the findings for graphical representation.
Within this study, we delve into novel optical solitons concerning the perturbed nonlinear Schrödinger equation, which governs the propagation of electromagnetic waves in magneto-optic waveguides. These components play vital roles in optical transmission lines and lasers, serving critical functions within integrated optical circuits as circulators, modulators, and isolators. Employing the simplest equation method, the 1φ(δ),φ′(δ)φ(δ)\left(\phantom{\rule[-0.75em]{}{0ex}},\frac{1}{\varphi \left(\delta )},\frac{\varphi ^{\prime} \left(\delta )}{\varphi \left(\delta )}\right) method, and the generalized Riccati equation mapping method, we derive single and multi-optical soliton solutions. Our analysis yields a diverse array of solutions, including multi-soliton, singular, combo bright-dark, periodic singular, bright, and dark optical solitons. Additionally, we discuss the parametric conditions crucial for both the existence and shaping of these solitons. The visual representation of our findings through three-dimensional, two-dimensional, and contour plots elucidates the dynamic phenomena and interprets the physical implications of these solutions using various parameter values. This research demonstrates the efficacy of rational analytical methods in elucidating the intricate dynamics of soliton solutions in nonlinear optical systems, thereby offering valuable insights for further exploration in the fields of physics, mathematics, sciences, and engineering.
