Mathematics

In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used in a C# environment to simulate the interaction between freak waves and bottom-fixed structures by establishing a fluid dynamics model. Paraview software 5.10.1 was used to analyze and visualize the simulation results. In order to simulate wave propagation accurately, the reliability of the model was verified by comparing experimental and simulated data. A two-dimensional numerical wave flume was established based on the SPH method, a conservative Riemann solver was introduced, a repulsive boundary condition was adopted, and a slope was used to eliminate wave reflection. Bottom-fixed structures of different heights and lengths, as well as different wave conditions, were selected to numerically simulate the interaction between freak waves and bottom-fixed structures. The results show that the height of bottom-fixed structures and wave conditions have a significant effect on hindering the propagation of rogue waves, while the length has little effect on the propagation of deformed waves. When the amplitude of the wave remains constant, both the period andthe duration of the deformed wave are longer. This research is of certain significance for the prediction of freak waves in marine engineering and the application and promotion of SPH methods. Full article

Although the impact of government subsidies on private innovation has been widely recognized and researched in numerous studies, few have considered the increasingly prevalent phenomenon of supply chain encroachment in their analysis. This paper explores this phenomenon through a game-theoretic model that takes into account a government entity, a supplier, and a manufacturer. The primary aim is to understand how the government can make optimal subsidy decisions when the supplier moves into the supply chain. Several interesting conclusions have been drawn: (1) under governmental innovation subsidies, the supplier will raise the price of the new technology to obtain more potential revenue, which is termed the inverse wholesale price effect; (2) different kinds of innovation subsidies are shown to have varied effects on R&D, production, and consumption behavior; and (3) different subsidy strategies are made compatible with the characteristics of innovative activities to maximize social welfare as much as possible. These findings shed light on inconsistent results surrounding the impacts of government subsidies on private innovations in the existing literature, providing municipalities with helpful guidance when encouraging private innovation initiatives amid supply chain encroachment. Full article

Improving the productivity and reliability of mining infrastructure is an important task contributing to the mining performance enhancement of any enterprise. Open-pit dump trucks that move rock masses from the mining site to unloading points are an important part of the infrastructure of coal mines, and they are the main transport unit used in the technological cycle during open-pit mining. The failure of any of the mining truck systems causes unscheduled downtime and leads to significant economic losses, which are associated with the need to immediately restore the working state and lost profits due to decreased site productivity and a disruption of the production cycle. Therefore, minimizing the number and duration of unscheduled repairs is a necessity. The most time-consuming operations are the replacement of the diesel engine, traction generator, and traction motors, which requires additional disassembly of the dump truck equipment; therefore, special reliability requirements are imposed on these units. In this article, a mathematical model intended for processing the statistical data was developed to determine the reliability indicators of the brush collector assembly and the residual life of brushes of electric motors, which, unlike existing models, allow the determination of the refined life of the brushes based on the limiting height of their wear. A method to predict the residual life of an electric brush of a DC electric motor is presented, containing a list of controlled reliability indicators that are part of the mathematical model. Using the proposed mathematical model, the reliability of the brush-collector assembly, the minimum height of the brush during operation, and the average rate of its wear were studied and calculated. Full article

In this paper, we study the dynamic behavior of an impulse differential chaotic system which can be applied to image encryption. Combined with the chaotic characteristics of the high dimensional impulsive differential equations, the plaintext image can be encrypted by using the traditional Henon map and diffusion sequences encryption algorithm. The initial values and control parameters serve as keys for encryption algorithms, and the algorithm has a larger key space. The key is resistant to minor interference and the accuracy can reach ${10}^{-12}$. The simulation results show that the impulsive differential chaotic system has a good application prospect in image encryption. Full article

We utilize quasi-subordination to analyze and introduce several new classes, and we construct a new operator by combining the error function and q-convolution. Additionally, we obtain estimates for the Fekete Szego functional and the Taylor–Maclaurin coefficients for functions in $\left|c_2\right|$ and $\left|c_3\right|$ new classes. Moreover, we discuss some applications of the operator. Full article

The fault maintenance scenario in coal-mine equipment intelligence is composed of videos, images, signals, and repair process records. Text data are not the primary data that reflect the fault phenomenon, but rather the secondary processing based on operation experience. Focusing on the difficulty of extracting fault knowledge from the limited textual maintenance process records, a forward static full-connected topology network modeling method based on domain knowledge from four dimensions of physical structure, internal association, condition monitoring, and fault maintenance, is proposed to increase the efficiency of constructing a fault-maintenance knowledge graph. Accurately identifying the intrinsic correlation between the equipment anomalies and the faults’ causes through only domain knowledge and loosely coupled data is difficult. Based on the static full-connected knowledge graph of the cantilever roadheader, the information entropy and density-based DBSCAN clustering algorithm is used to process and analyze many condition-monitoring historical datasets to optimize the entity relationships between the fault phenomena and causes. The improved DBSCAN algorithm consists of three stages: firstly, extracting entity data related to fault information from the static fully connected graph; secondly, calculating the information entropy based on the real dataset describing the fault information and the historical operating condition, respectively; and thirdly, comparing the entropy values of the entities and analyzing the intrinsic relationship between the fault phenomenon, the operating condition data, and the fault causes. Based on the static full-connected topology storage in the Neo4j database, the information entropy and density-based DBSCAN algorithm is computed by using Python to identify the relationship weights and dynamically display optimized knowledge graph topology. Finally, an example of EBZ200-type cantilever roadheader for smart maintenance is studied to analyze and evaluate the forward and four-mainlines knowledge graph modeling method and the dynamic entity relations optimization method for static full-connected knowledge graph. Full article

This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed. Full article

In this paper, a system of four coupled van der Pol oscillators with delay is studied. Firstly, the conditions for the existence of multiple periodic solutions of the system are given. Secondly, the multiple periodic solutions of spatiotemporal patterns of the system are obtained by using symmetric Hopf bifurcation theory. The normal form of the system on the central manifold and the bifurcation direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are attached to demonstrate our theoretical results. Full article

This study investigates the complex interplay between public sentiment, as captured through news titles and descriptions, and the stock prices of three major tech companies: Microsoft (MSFT), Tesla (TSLA), and Apple (AAPL). Leveraging advanced analytical methods including Pearson correlation, wavelet coherence, and regression analysis, this research probes the degree to which stock-price fluctuations can be attributed to the polarity of media sentiment. The methodology combines statistical techniques to assess sentiment’s predictive power for stock opening and closing prices, while wavelet coherence analysis unveils the temporal dynamics of these relationships. The results demonstrate a significant correlation between sentiment polarity and stock prices, with description polarity affecting Microsoft’s opening prices, title polarity influencing Tesla’s opening prices, and a positive impact of title polarity on Apple’s closing prices. However, Tesla’s stock showed no significant coherence, indicating a potential divergence in how sentiment affects stock behavior across companies. The study highlights the importance of sentiment analysis in forecasting stock-market trends, revealing not only direct correlations but also lagged influences on stock prices. Despite its focus on large-cap tech firms, this research provides a foundational understanding of sentiment’s financial implications, suggesting further investigation into smaller firms and other market sectors. Full article

The pursuit of environmental sustainability, energy conservation, and emissions reduction has become a global focal point. Electricity is the primary source of energy in our daily lives. Through the analysis of smart power systems, we can efficiently and sustainably harness electrical energy. However, electric power system data inherently contain a wealth of sensitive user information. Therefore, our primary concern is protecting these sensitive user data while performing precise and effective analysis. To address this issue, we have innovatively proposed three granular information models based on differential privacy. In consideration of the characteristics of enterprise electricity consumption data and the imperative need for privacy protection, we implement a reasonable modeling process through data processing, information granulation expression, and the optimization analysis of information granularity. Our datasets encompass enterprise electricity consumption data and related attributes from Hitachi Building Technology (Guangzhou) Co., Ltd’s cloud computing center. Simultaneously, we have conducted experiments using publicly available datasets to underscore the model’s versatility. Our experimental results affirm that granular computation can improve the utility of differential privacy in safeguarding data privacy. Full article

The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus can be equivalently transformed into the output stability regardless of whether the associated signed digraphs are structurally balanced or not. By taking advantage of the standard robust $H_{\infty }$ control theory, the bipartite consensus and state stability results can be built for signed networks under structurally balanced and unbalanced conditions, respectively, in which the desired disturbance rejection performances can also be satisfied. Furthermore, the mathematical expression can be given for the terminal states of signed networks under the influence of external disturbances. In addition, two simulations are presented to verify the correctness of our developed results. Full article

Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks and is an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node centralities for network dismantling with effective node removal strategies from the literature, namely betweenness, closeness, degree, and k-shell node removal, for synthetic and real-world networks. We evaluate the dismantling of the network by using the size of the largest connected component (LCC). We find that the degree nodes attack is the best strategy overall, and the new node removal strategies based on RW show the highest efficacy in regard to peculiar network topology. Specifically, RW strategy based on covering time emerges as the most effective strategy for a synthetic lattice network and a real-world road network. Our results may help researchers select the best node attack strategies in a specific network class and build more robust network structures. Full article

Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is less information in current status data than in right censored data and interval censored data. This paper considers the Weibull PH model under the current status data and introduces the Poisson latent variables to augment the data, then uses the expectation-maximization (EM) algorithm to obtain the maximum likelihood estimators of the model parameters. The EM algorithm is compared with the Newton–Raphson (NR) algorithm from several perspectives in the simulation studies, and the results show that the proposed method has several highlights, such as computational simplicity, improved convergence stability, and overall estimator results that are either comparable or slightly better in terms of bias. Furthermore, the performance of the Weibull PH model and the semi-parametric PH model is compared under two simulation scenarios, and two standard model selection criteria are used for model selection. The results indicate that the Weibull PH model has significant advantages when failure time follows a Weibull distribution. Lastly, the Weibull PH model along with EM algorithm is applied to lung tumor data and intraocular lens (IOL) calcification data with the aim of assessing the impact of covariates, including environmental factors and gender, on event timing and risk. Full article

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria. Full article

In the present work, we concentrate on a certain class of nonlinear difference equations and propose sufficient conditions for the existence of their almost automorphic solutions. In our analysis, we invert an appropriate mapping and obtain the main existence outcomes by utilizing the contraction mapping principle. As the second objective of the manuscript, we reconsider one of the landmark results, namely the Bohr–Neugebauer theorem, in the qualitative theory of dynamical equations, and we investigate the relationship between the existence of almost automorphic solutions and the existence of solutions with a relatively compact range for the proposed difference equation type. Thus, we provide a discrete counterpart of the Bohr–Neugebauer theorem due to the almost automorphy notion under some technical conditions. Full article

With the proliferation of blockchain technology in decentralized applications like decentralized finance and supply chain and identity management, smart contracts operating on a blockchain frequently encounter security issues such as reentrancy vulnerabilities, timestamp dependency vulnerabilities, tx.origin vulnerabilities, and integer overflow vulnerabilities. These security concerns pose a significant risk of causing substantial losses to user accounts. Consequently, the detection of vulnerabilities in smart contracts has become a prominent area of research. Existing research exhibits limitations, including low detection accuracy in traditional smart contract vulnerability detection approaches and the tendency of deep learning-based solutions to focus on a single type of vulnerability. To address these constraints, this paper introduces a smart contract vulnerability detection method founded on multimodal feature fusion. This method adopts a multimodal perspective to extract three modal features from the lifecycle of smart contracts, leveraging both static and dynamic features comprehensively. Through deep learning models like Graph Convolutional Networks (GCNs) and bidirectional Long Short-Term Memory networks (bi-LSTMs), effective detection of vulnerabilities in smart contracts is achieved. Experimental results demonstrate that the proposed method attains detection accuracies of 85.73% for reentrancy vulnerabilities, 85.41% for timestamp dependency vulnerabilities, 83.58% for tx.origin vulnerabilities, and 90.96% for integer Overflow vulnerabilities. Furthermore, ablation experiments confirm the efficacy of the newly introduced modal features, highlighting the significance of fusing dynamic and static features in enhancing detection accuracy. Full article

Background: Electrodermal activity (EDA) serves as a prominent biosignal for assessing sympathetic activation across various scenarios. Prior research has suggested a connection between EDA and fluctuations in Parkinson’s disease (PD), but its precise utility in reliably detecting these fluctuations has remained unexplored. This study aims to evaluate the efficacy of both basic and advanced analyses of EDA changes in identifying the transition to the ON state following dopaminergic medication administration in individuals with PD. Methods: In this observational study, 19 individuals with PD were enrolled. EDA was continuously recorded using the Empatica E4 device, worn on the wrist, during the transition from the OFF state to the ON state following levodopa intake. The raw EDA signal underwent preprocessing and evaluation through three distinct approaches. A logistic regression model was constructed to assess the significance of variables predicting the ON/OFF state, and support vector machine (SVM) models along with various Neural Network (NN) configurations were developed for accurate state prediction. Results: Differences were identified between the ON and OFF states in both the time and frequency domains, as well as through the utilization of convex optimization techniques. SVM and NN models demonstrated highly promising results in effectively distinguishing between the OFF and ON states. Conclusions: Evaluating sympathetic activation changes via EDA measures holds substantial promise for detecting non-motor fluctuations in PD. The SVM algorithm, in particular, yields precise outcomes for predicting these non-motor fluctuation states. Full article

In this article, we introduce a new subgradient extra-gradient algorithm to find the common element of a set of fixed points of a Bregman relatively nonexpansive mapping and the solution set of an equilibrium problem involving a Pseudomonotone and Bregman–Lipschitz-type bifunction in reflexive Banach spaces. The advantage of the algorithm is that it is run without prior knowledge of the Bregman–Lipschitz coefficients. Finally, two numerical experiments are reported to illustrate the efficiency of the proposed algorithm. Full article

In this article, two kinds of local and parallel stabilized finite element methods based upon two grid discretizations are proposed and investigated for the Stokes–Darcy model. The lowest equal-order finite element pairs (${\mathbf{P}}_1$-$P_1$-$P_1$) are taken into account to approximate the velocity, pressure, and piezometric head, respectively. To circumvent the inf-sup condition, the stabilized term is chosen as the difference between a consistent and an under-integrated mass matrix. The proposed algorithms consist of approximating the low-frequency component on the global coarse grid and the high-frequency component on the local fine grid and assembling them to obtain the final approximation. To obtain a global continuous solution, the technique tool of the partition of unity is used. A rigorous theoretical analysis for the algorithms was conducted and numerical experiments were carried out to indicate the validity and efficiency of the algorithms. Full article