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In the present paper, we introduce the concept of idempotent-aided factorization (I.-A. factorization) of a regular element of a semigroup, which can be understood as a semigroup-theoretical extension of full-rank factorization of matrices over a field. I.-A. factorization of a regular element d is defined by means of an idempotent e from its Green’s D-class as decomposition into the product d=uv, so that the element u belongs to the Green’s R-class of the element d and the Green’s L-class of the idempotent e, while the element v belongs to the Green’s L-class of the element d and the Green’s R-class of the idempotent e. The main result of the paper is a theorem which states that each regular element of a semigroup possesses an I.-A. factorization with respect to each idempotent from its Green’s D-class. In addition, we prove that when one of the factors is given, then the other factor is uniquely determined. I.-A. factorizations are then used to provide new existence conditions and characterizations of group inverses and (b,c)-inverses in a semigroup. In our further research, these factorizations will be applied to matrices with entries in a field, and efficient algorithms for realization of such factorizations will be provided.

Market competitiveness drives the electric motors industry, which in turn necessitates the selection of optimal production scenarios, particularly in the context of packaging. This is crucial for maintaining competitiveness and meeting the rigorous quality and logistical demands that are characteristic of this industry. This paper presents a systematic analysis of the packaging production chain for electric motors, employing the SAPEVO-M method as a decision aid tool. The study examines various strategic options, including outsourcing and internalizing processes, with a particular focus on their impacts on logistics, quality control, and overall supply-chain efficiency. The research conducts a comprehensive evaluation of these strategies to ascertain the most effective approach for managing the complexities of packaging production. The SAPEVO-M method facilitated a structured decision-making process, allowing for the aggregation and prioritization of diverse criteria such as cost, quality, flexibility, environmental impact, and supply risk. A sensitivity analysis was performed to validate the robustness of the decision-making outcomes under varying alternatives. The findings highlight the benefits of internalizing certain processes, particularly the assembly (with a score of 43.27%), to gain direct control over production variables, leading to enhanced operational efficiency and product competitiveness. This paper contributes to the literature by demonstrating the application of MCDA in enhancing strategic decisions within the electric motors industry, providing insights for analyzing other manufacturing factors in the improvement of supply-chain processes.

This paper explores the challenges of finding robust shortest paths in multimodal transportation networks. With the increasing complexity and uncertainties in modern transportation systems, developing efficient and reliable routing strategies that can adapt to various disruptions and modal changes is essential. By incorporating practical constraints in parameter uncertainty, this paper establishes a robust shortest path mixed-integer programming model based on a multimodal transportation network under transportation time uncertainty. To solve robust shortest path problems with multimodal transportation, we propose a modified Dijkstra algorithm that integrates parameter uncertainty with multimodal transportation. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments on test sets of different scales and a comparison of the runtime using a commercial solver. The experimental results on the multimodal transportation networks demonstrate the effectiveness of our approach in providing robust and efficient routing solutions. The results demonstrate that the proposed method can generate optimal solutions to the robust shortest path problem in multimodal transportation under time uncertainty and has practical significance.

This paper proposes a highly secure image encryption technique based on chaotic synchronization. Firstly, through the design of a synchronization controller, we ensure that the master–slave chaotic extremum-coded random number generators (ECRNGs) embedded in separated transmitters and receivers are fully synchronized to provide synchronized dynamic random sequences for image encryption applications. Next, combining these synchronized chaotic sequences with the AES encryption algorithm, we propose an image segmentation and multi-encryption method to enhance the security of encrypted images and realize a secure image transmission system. Notably, in the design of the synchronization controller, the transient time before complete synchronization between the master and slave ECRNGs is effectively controlled by specifying the eigenvalues of the matrix in the synchronization error dynamics. Research results in this paper also show that complete synchronization of ECRNGs can be achieved within a single sampling time, which significantly contributes to the time efficiency of the image transmission system. As for the image encryption technique, we propose the method of image segmentation and use the synchronized dynamic random sequences generated by the ECRNGs to produce the keys and initialization vectors (IVs) required for AES-CBC image encryption, greatly enhancing the security of the encrypted images. To highlight the contribution of the proposed segmented image encryption, statistical analyses are conducted on the encrypted images, including histogram analysis (HA), information entropy (IE), correlation coefficient analysis (CCA), number of pixels change rate (NPCR), and unified average changing intensity (UACI), and compared with existing literature. The comparative results fully demonstrate that the proposed encryption method significantly enhances image encryption performance. Finally, under the network transmission control protocol (TCP), the synchronization of ECRNGs, dynamic keys, and IVs is implemented as well as segmented image encryption and transmission, and a highly secure image transmission system is realized to validate the practicality and feasibility of our design.

The paper considers a bidimensional continuous-time risk model with subexponential claims and Brownian perturbations, in which the price processes of the investment portfolio of the two lines of business are two geometric Lévy processes and the two lines of business share a common claim-number process, which is a renewal counting process. The paper mainly considers the claims of each line of business having a dependence structure. When the claims have subexponential distributions, the asymptotics of the finite-time ruin probabilities ψand(x1,x2;T) and ψsim(x1,x2;T) have been obtained. When the distributions of claims belong to the intersection of long-tailed and dominatedly varying-tailed distribution classes, the asymptotics of the finite-time ruin probability ψor(x1,x2;T) is given.

This paper focuses on event-triggered state estimation and control of positive complex networks. An event-triggered condition is provided for discrete-time complex networks by which an event-based state estimator and an estimator-based controller are designed through matrix decomposition technology. Thus, the system is converted to an interval uncertain system. The positivity and the L1-gain stability of complex networks are ensured by resorting to a co-positive Lyapunov function. All conditions are solvable in terms of linear programming. Finally, the effectiveness of the proposed state estimator and controller are verified by a numerical example. The main contributions of this paper are as follows: (i) A positive complex network framework is constructed based on an event-triggered strategy, (ii) a new state estimator and an estimator-based controller are proposed, and (iii) a simple analysis and design approach consisting of a co-positive Lyapunov function and linear programming is presented for positive complex networks.

This paper presents a comprehensive framework for implementing digital twins in aircraft lifecycle management, with a focus on using data-driven models to enhance decision-making and operational efficiency. The proposed framework integrates cutting-edge technologies such as IoT sensors, big data analytics, machine learning, 6G communication, and cloud computing to create a robust digital twin ecosystem. This paper explores the key components of the framework, including lifecycle phases, new technologies, and models for digital twins. It discusses the challenges of creating accurate digital twins during aircraft operation and maintenance and proposes solutions using emerging technologies. The framework incorporates physics-based, data-driven, and hybrid models to simulate and predict aircraft behavior. Supporting components like data management, federated learning, and analytics tools enable seamless integration and operation. This paper also examines decision-making models, a knowledge-driven approach, limitations of current implementations, and future research directions. This holistic framework aims to transform fragmented aircraft data into comprehensive, real-time digital representations that can enhance safety, efficiency, and sustainability throughout the aircraft lifecycle.

The shortest path problem is fundamental in graph theory and has been studied extensively due to its practical importance. Despite this aspect, finding the shortest path between two nodes remains a significant challenge in many applications, as it often becomes complex and time consuming. This complexity becomes even more challenging when constraints make the problem non-additive, thereby increasing the difficulty of finding the optimal path. The objective of this paper is to present a broad perspective on the conventional shortest path problem. It introduces a new method to classify cost functions associated with graphs by defining distinct sets of cost functions. This classification facilitates the exploration of line graphs and an understanding of the upper bounds on the transformation sizes for these types of graphs. Based on these foundations, the paper proposes a practical methodology for solving non-additive shortest path problems. It also provides a proof of optimality and establishes an upper bound on the algorithmic cost of the proposed methodology. This study not only expands the scope of traditional shortest path problems but also highlights their computational complexity and potential solutions.

In various applications, observed variables are missing some information that was intended to be collected. The estimations of both loading and path coefficients could be biased when ignoring the missing data. Inverse probability weighting (IPW) is one of the well-known methods helping to reduce bias in regressions, while belonging to a promising but new category in structural equation models. The paper proposes both parametric and nonparametric IPW estimation methods for dynamic structural equation models, in which both loading and path coefficients are developed into functions of a random variable and of the quantile level. To improve the computational efficiency, modified parametric IPW and modified nonparametric IPW are developed through reducing inverse probability computations but making fuller use of completely observed information. All the above IPW estimation methods are compared to existing complete case analysis through simulation investigations. Finally, the paper illustrates the proposed model and estimation methods by an empirical study on digital new-quality productivity.

Based on the project portfolio selection and scheduling problem (PPSS), the development of a systematic and scientific project scheduling plan necessitates comprehensive consideration of individual preferences and multiple realistic constraints, rendering it an NP-hard problem. Simultaneously, accurately and swiftly evaluating the value of projects as a complex entity poses a challenging issue that requires urgent attention. This paper introduces a novel qualitative evaluation-based project value assessment process that significantly reduces the cost and complexity of project value assessment, upon which a preference-based deep reinforcement learning method is presented for computing and solving project subsets and time scheduling plans. This paper first determines the key parameter values of the algorithm through specific examples. Then, using the method of controlling variables, it explores the sensitivity of the algorithm to changes in problem size and dimensionality. Finally, the proposed algorithm is compared with two classical algorithms and two heuristic algorithms across different instances. The experimental results demonstrate that the proposed algorithm exhibits higher effectiveness and accuracy.

Composition formula is one of the most important research topics in functional analysis theory. Various relationships can be obtained using the composition formula. Since the generalized Brownian motion process used in this paper has a non-zero mean function, there are many restrictions on obtaining a composition formula for the modified analytic function space Fourier–Feynman transform. This paper contains an idea of how the composition Formula (9) below is established for the modified analytic function space Fourier–Feynman transform on function space. Using this idea, we are able to solve a problem that had never been solved before.

In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds.

In this paper, a new analytic expression for the frequency of vibration of a strong nonlinear polynomial-type oscillator is introduced. The method for frequency calculation is based on the transformation of the nonlinear oscillators into linear ones using the equality of their amplitudes and periods of vibration. The frequency of the linear oscillator is assumed to be the sum of frequencies corresponding to each nonlinearity in the original oscillator separately, i.e., the sum of frequencies of truly nonlinear oscillators. The obtained frequency is a complex function of amplitude, coefficient and order of nonlinearity. For simplification, the frequencies of the truly nonlinear oscillators are modified as power order functions of the exact frequency of the cubic oscillator which is linearly dependent on the amplitude of vibration. In this paper, the approximate frequency expression is developed for the harmonic any-order nonlinear oscillator and oscillators with the sum of polynomial nonlinearities. The accuracy of the obtained frequencies is tested on the examples of non-integer order nonlinear oscillators and also on a quadratic-cubic oscillator. The difference between the analytical and exact, numerically obtained results is negligible. The suggested approximate frequency expression has a simple algebraic form and is suitable for application by engineers and technicians.

In the e-commerce last-mile delivery process, the asset operators (logistics service providers who own parcel locker facilities) support their delivery service with parcel lockers, while the non-asset operators (logistics service providers without parcel lockers) perform door-to-door delivery. Due to demand fluctuation, asset operators’ parcel-locker slots may be left vacant, while non-asset operators are stuck with the high-cost door-to-door service. The exclusiveness of parcel-locker usage reduces resource utilization and service efficiency in last-mile delivery. Therefore, this paper proposes a parcel-locker-sharing model in which these two parties share the parcel-locker capacity in last-mile delivery. The asset operator rents the unused parcel lockers to the non-asset operator by charging a rental fee,while the non-asset operator rents the parcel lockers for delivery to save logistics costs. The motivation of this alliance is to increase the profits of both parties and that of the total supply chain. This study establishes the supply-chain profit model for the parcel-locker-sharing framework and finds that the profit or loss depends on the comparison of the operation cost savings and delivery-cost savings. A numerical analysis is conducted to validate the final result. The research further suggests the optimal rental quantity and price interval. This paper is the first to study the operational mechanism of sharing the parcel locker between two distinct types of logistics service providers and to offer recommendations for industrial application.

This paper presents a new numerical scheme for a class of linear impulsive neutral differential equations with constant coefficients based on the Euler method. We rigorously establish the first-order convergence of the proposed numerical approach. Additionally, the asymptotical stability of the exact solutions and numerical solutions of impulsive neutral differential equations are studied. To substantiate our findings, two illustrative examples are provided, demonstrating the theoretical conclusions of this paper.

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.

This paper presents a comprehensive study of the linguistic Z-graph, which is a novel framework designed to analyze linguistic structures within social networks. By integrating concepts from graph theory and linguistics, the linguistic Z-graph provides a detailed understanding of language dynamics in online communities. This study highlights the practical applications of linguistic Z-graphs in identifying central nodes within social networks, which are crucial for online businesses in market capture and information dissemination. Traditional methods for identifying central nodes rely on direct connections, but social network connections often exhibit uncertainty. This paper focuses on using fuzzy theory, particularly linguistic Z-graphs, to address this uncertainty, offering more detailed insights compared to fuzzy graphs. Our study introduces a new centrality measure using linguistic Z-graphs, enhancing our understanding of social network structures.

In some settings, systems may not fail completely but instead undergo performance degradation, leading to reduced efficiency. A significant concern arises when a system transitions into a degraded state without immediate detection, with the degradation only becoming apparent after an unpredictable period. Undetected degradation can result in failures with significant consequences. For instance, a minor crack in an oil pipeline might go unnoticed, eventually leading to a major leak, environmental harm, and costly cleanup efforts. Similarly, in the nuclear industry, undetected degradation in reactor cooling systems could cause overheating and potentially catastrophic failure. This paper focuses on reliability modeling for systems experiencing degradation, accounting for time delays associated with undetected degraded states, self-repair mechanisms, and varying operating environments. The paper presents a reliability model for degraded, time-dependent systems, incorporating various aspects of degradation. It first discusses the model assumptions and formulation, followed by numerical results obtained from system modeling using the developed program. Various scenarios are illustrated, incorporating time delays and different parameter values. Through computational analysis of these complex systems, we observe that the probability of the system being in the undetected degraded state tends to stabilize shortly after the initial degradation begins. The model is valuable for predicting and establishing an upper bound on the probability of the undetected, degraded state and the system’s overall reliability. Finally, the paper outlines potential avenues for future research.

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to dψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field.

Since SQL injection allows attackers to interact with the database of applications, it is regarded as a significant security problem. By applying machine learning algorithms, SQL injection attacks can be identified. Problem: In the training stage of machine learning methods, effective features are used to develop an optimal classifier that is highly accurate. The specification of the features with the highest efficacy is considered to be an NP-complete combinatorial optimization challenge. Selecting the most effective features refers to the procedure of identifying the smallest and most effective features in the dataset. The rationale behind this paper is to optimize the accuracy, precision, and sensitivity parameters of the SQL injection attack detection method. Method: In this paper, a method for identifying SQL injection attacks was suggested. In the first step, a particular training dataset that included 13 features was developed. In the second step, to specify the best features of the dataset, a specific binary variety of the Olympiad optimization algorithm was developed. Various machine learning algorithms were used to create the optimal attack detector. Results: Based on the experiments carried out, the suggested SQL injection detector using an artificial neural network and the feature selector can achieve 99.35% accuracy, 100% precision, and 100% sensitivity. Owing to selecting about 30% of the effective features, the proposed method enhanced the efficacy of SQL injection detectors.

In the context of the high-speed development of 5G communications, high-performance decoding schemes for polar codes are a hot spot in channel coding research. Shift pruning successive cancellation list (SP-SCL) decoding aims to recover the correct path by shift pruning in the extra SCL decoding. However, the current SP-SCL decoding is inflexible in determining the shift positions. In this paper, a flexible shift pruning SCL (FSP-SCL) decoding is proposed. Firstly, the reasons for movement and the eliminated states of the correct path are analyzed in detail using the path metric range (PMR), and on this basis, the validity of the method adopted in this paper for determining the shift priority of the information bits is verified. Secondly, the FSP-SCL decoding proposes two methods for determining the shift positions. One is the log-likelihood ratio (LLR) threshold method, which compares the LLR values of the eliminated paths on the shift bit with the corresponding LLR threshold to determine the shift positions. The other is the path distance method. It combines the minimum distance between the eliminated paths and the received vector with the path metrics to determine the shift positions. Both methods are more flexible and practical, as they can calculate the corresponding shift positions online based on a specific shift bit, avoiding the high complexity caused by the simulation method. Finally, this paper designs various experimental schemes to verify the decoding performance of the FSP-SCL. The experimental results show that in terms of error-correction performance, the LLR threshold-based FSP-SCL (FSPL (LLR threshold)) decoding, the path distance-based FSP-SCL (FSPL (path distance)) decoding and the existing SP-SCL decoding are roughly equal overall. In terms of decoding complexity, FSPL (LLR threshold) decoding is slightly better than FSPL (path distance) decoding, and the decoding complexity of both is lower than that of SP-SCL decoding, with the difference being more pronounced in the medium to high SNR regions.

This paper presents an estimation of the launching points of unmanned aerial vehicles (UAVs) equipped with boosters. When UAVs are detected and tracked by sensors such as radars, the fast identification of vehicle launching points is needed for air traffic control and defense systems. When UAVs in a boosting phase are controlled by first-order pitch programming, this paper leverages inverse first-order pitch programming to analytically solve launching points. Furthermore, a two-point robust measurement selection (T-RMS) scheme is developed to reduce errors such as random noise and bias by utilizing multiple moving average filters. The proposed work is verified by various simulation results.

This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed.

In this paper, we propose a representation of the visual information about Multiplayer Online Battle Arena (MOBA) video games using an adapted unsupervised deep learning architecture called Convolutional Accordion Auto-Encoder (Conv_A2E). Our study includes a presentation of current representations of MOBA video game information and why our proposal offers a novel and useful solution to this task. This approach aims to achieve dimensional reduction and refined feature extraction of the visual data. To enhance the model’s performance, we tested several attention mechanisms for computer vision, evaluating algorithms from the channel attention and spatial attention families, and their combination. Through experimentation, we found that the best reconstruction of the visual information with the Conv_A2E was achieved when using a spatial attention mechanism, deformable convolution, as its mean squared error (MSE) during testing was the lowest, reaching a value of 0.003893, which means that its dimensional reduction is the most generalist and representative for this case study. This paper presents one of the first approaches to applying attention mechanisms to the case study of MOBA video games, representing a new horizon of possibilities for research.

This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach’s performance and one-sample lifetime data are presented to illustrate the proposed methodology.

Moran’s I is a spatial autocorrelation measure of univariate spatial data. Therefore, even if p spatial data exist, we can only obtain p values for Moran’s I. In other words, Moran’s I cannot measure the degree of spatial autocorrelation of multivariate spatial data as a single value. This paper addresses this issue. That is, we extend Moran’s I so that it can measure the degree of spatial autocorrelation of multivariate spatial data as a single value. In addition, since the local version of Moran’s I has the same problem, we extend it as well. Then, we establish their properties, which are fundamental for applied work. Numerical illustrations of the theoretical results obtained in the paper are also provided.

This paper explores secure communication systems with a chaotic carrier. The use of chaotic oscillations instead of regular van der Pol oscillators as a signal carrier is a promising and active research area, providing not only communication systems with new protection principles and organization but also high steganographic efficiency when transmitting short messages. The problem is to select methods and techniques for mixing a useful signal into a chaotic one and its recovery on the receiver side, featuring a set of properties acceptable for implementation and real-world application. We demonstrate application of synergetic control theory (SCT), which provides advanced observer-basing methods for nonlinear dynamic systems as well as explore example of data transmission system consisting of a Genesio–Tesi chaotic oscillator, data signal transmission with a method of nonlinear modulation, and recovering with a single-channel synergetic observer at the receiver side. The paper presents a nonlinear state observer modeling procedure followed by building a MATLAB/Simulink simulation model of the data transmission system for the PC-platform along with software implementation for the Raspberry Pi platform, with simulation and experimental run results showing data transmission rates seem to be acceptable for the considered practical applications. Practical applications and limitations issues are discussed. Future research will be universal modeling procedures for different classes of chaotic generators and whole system experimental hardware implementation. The obtained results can be primarily used in short messages and/or encryption keys secure transmission systems, cyber-physical system component command communications, as well as chaotic carrier system R&D competitive studies and other applications.

This paper presents the topological derivative of the first eigenvalue for the free vibration model of plane structures. We conduct a topological asymptotic analysis to account for perturbations in the domain caused by inserting a small inclusion. The paper includes a rigorous derivation of the topological derivative for the eigenvalue problem along with a proof of its existence. Additionally, we provide numerical examples that illustrate the application of the proposed methodology for maximizing the first eigenvalue in plane structures. The results demonstrate that multiple eigenvalues were not encountered.

With the advent of big data, the swift advancement of diverse algorithmic technologies has enhanced the transaction efficiency of the e-commerce business. Nevertheless, it is crucial to acknowledge that e-commerce platforms might employ algorithmic technology to enforce differential pricing for various consumers with the aim of maximizing profits, thus infringing upon the lawful rights and interests of consumers. This paper focuses on the algorithmic price discrimination commonly observed on e-commerce platforms. To effectively regulate this behavior, the paper utilizes evolutionary game theory (EGT) to analyze the strategies employed by e-commerce platforms, consumers, and market regulators to achieve stability. This research employs a real-life situation and utilizes parametric simulation to visualize and analyze the process and outcomes of the three-party evolutionary game. The results demonstrate the credibility and feasibility of the article’s findings. Based on our research, we have reached the following findings: During the process of evolution, the strategic decisions made by the game participants from the three parties will mutually impact each other, and various elements exert varying degrees of influence on the strategic choices made by the game participants from each party. Collaborative governance can enable consumers and market regulators to regulate the discriminatory pricing behavior of e-commerce platforms effectively. This article offers valuable insights into the governance of violations in the e-commerce sector based on robust data and model research.

The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire. Since then, a considerable number of papers on Roman {2}-domination and its variants have been published. In this paper, we survey published results on Roman {2}-domination as well as the main findings on Roman {2}-domination variants found in the literature. A list of open problems related to this notion and its variants are also given.

Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category prototypes to enhance the generalization ability of the models. Therefore, this paper proposes a prototype network-based named entity recognition (NER) method, namely the FSPN-NER model, to solve the problem of difficult recognition of sensitive data in data-sparse text. The model utilizes the positional coding model (PCM) to pre-train the data and perform feature extraction, then computes the prototype vectors to achieve entity matching, and finally introduces a boundary detection module to enhance the performance of the prototype network in the named entity recognition task. The model in this paper is compared with LSTM, BiLSTM, CRF, Transformer and their combination models, and the experimental results on the test dataset show that the model outperforms the comparative models with an accuracy of 84.8%, a recall of 85.8% and an F1 value of 0.853.

This is the third installment in a series of papers on a one-parameter extension of the Rogers–Ramanujan identities (this extension was discovered independently by Rogers and Ramanujan). In this paper, we report a new proof of this identity. Our key ingredient is the Bridge Lemma, an identity that connects the both sides of the one-parameter refinement, which differ significantly in terms of their complexity.

This paper introduces the improvements in natural-frequency-based SHM by applying bio-inspired optimization methods and a vision-based monitoring system for effective damage detection. This paper proposes a natural frequency extraction method using a motion magnification-based vision monitoring system with bio-inspired optimization techniques to estimate the damage location and depth in a cantilever beam. The proposed optimization techniques are inspired by natural processes and biological evolution including genetic algorithms, particle swarm optimization, sea lion optimization, and coral reefs optimization. To verify the performance of each bio-inspired optimization method, the eigenvalues of a two-bay truss structure are used for estimating the damaged elements. Then, using the proposed video motion magnification method, the natural frequency for each undamaged and damaged cantilever beam is extracted and compared with the LDV sensor to verify the proposed vision-based monitoring system. The performance of each bio-inspired optimizer in damage detection is compared. As a result, coral reefs optimization shows the lowest average error, around 1%, in damage detection using the natural frequency.

The 1st-level General Fractional Derivatives (GFDs) combine in one definition the GFDs of the Riemann–Liouville type and the regularized GFDs (or the GFDs of the Caputo type) that have been recently introduced and actively studied in the fractional calculus literature. In this paper, we first construct an operational calculus of the Mikusiński type for the 1st-level GFDs. In particular, it includes the operational calculi for the GFDs of the Riemann–Liouville type and for the regularized GFDs as its particular cases. In the second part of the paper, this calculus is applied for the derivation of the closed-form solution formulas to the initial-value problems for the linear fractional differential equations with the 1st-level GFDs.

In this paper we consider a system of linear bars, spherically jointed at their ends. For each bar one end is linked to the origin. We discuss the equations from which one obtains the deviation of the origin, and some possible optimizations concerning the minimum displacement of the origin and the minimum force in one bar, which are the main goals of the paper. The optimization is performed considering that for two bars one end is unknown; that is, the angles between the bars and the axes are unknown. It is proved that it is difficult to obtain an analytical solution in the general case, and the problem can be discussed only by numerical methods. A numerical case is also studied and some comments concerning the results are given.

Time-of-use pricing of electric energy, as an important part of the national policy of energy conservation and emission reduction, requires accurate electric energy data as support. However, due to various reasons, the electric energy data are often missing. To address this thorny problem, this paper constructs a CNN and GRU-based recovery model (RCNN-BiGRU) for electric energy data by taking the missing data as the output and the historical data of the neighboring moments as the input. Firstly, a convolutional network with a residual structure is used to capture the local dependence and periodic patterns of the input data, and then a bidirectional GRU network utilizes the extracted potential features to model the temporal relationships of the data. Aiming at the difficult selection of network structure parameters and training process parameters, an accelerated adaptive differential evolution (AADE) algorithm is proposed to optimize the electrical energy data recovery model. The algorithm designs an accelerated mutation operator and at the same time adopts an adaptive strategy to set the two key parameters. A large amount of real grid data are selected as samples to train the network, and the comparison results verify that the proposed combined model outperforms the related CNN and GRU networks. The comparison experimental results with other optimization algorithms also show that the AADE algorithm proposed in this paper has better data recovery performance on the training set and significantly better performance on the test set.

This paper proposes a decentralized adaptive event-triggered fault-tolerant cooperative control (ET-FTCC) scheme for multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults and external disturbances under denial-of-service (DoS) attacks. The multiple UAVs and UGVs have a larger search radius, which is important in both the civilian and military domains. The different dynamics between UAVs and UGVs result in unbalanced interactions in the communication topologies, which increases the complexity of cooperative control. DoS attacks are conducted in both sensor and control channels. The dynamic models of UAVs and UGVs are introduced firstly, and the unified heterogeneous multiagent system model with actuator faults is established. The composite observer is designed to obtain the information of state and lumped disturbance, which is used to design the controller. In order to save the limited communication network resources, the event-triggered mechanism is introduced. The transformed error is presented by using the prescribed performance function (PPF). Then, the sliding-mode manifold is presented by combining the event-triggered control scheme to achieve the tracking purpose with actuator faults, external disturbances, and DoS attacks. Based on the Lyapunov function approach, the tracking errors are bounded within the prescribed boundary. Finally, the effectiveness of the proposed method is verified by qualitative analysis and quantitative analysis of the simulation results. This study can enhance the security and reliability of heterogeneous multiagent systems, providing technical support for the safe operation of unmanned systems. This paper mainly solves the FTCC problem of second-order nonlinear heterogeneous multiagent systems, and further research is needed for the FTCC problem of higher-order nonlinear heterogeneous multi-agent systems. In addition, the system may encounter multiple cyber attacks. As one of the future research works, we can extend the results of this paper to high-order nonlinear systems under multiple cyber attacks, which contain DoS attacks and deception attacks, and achieve fault-tolerant cooperative control of heterogeneous multiagent systems.

This paper addresses the problem of making inferences about a common mean vector from several independent multivariate normal populations with unknown and unequal dispersion matrices. We propose an unbiased estimator of the common mean vector, along with its asymptotic estimated variance, which can be used to test hypotheses and construct confidence ellipsoids, both of which are valid for large samples. Additionally, we discuss an approximate method based on generalized p-values. The paper also presents exact test procedures and methods for constructing exact confidence sets for the common mean vector, with a comparison of the local power of these exact tests. The performance of the proposed methods is demonstrated through a simulation study and an application to data from the Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement 2021 conducted by the U.S. Census Bureau for the Bureau of Labor Statistics.

In order to address the challenge of the small-scale, small-target, and complex scenes often encountered in offshore remote sensing image datasets, this paper employs an interpolation method to achieve super-resolution-assisted target detection. This approach aligns with the logic of popular GANs and generative diffusion networks in terms of super-resolution but is more lightweight. Additionally, the image count is expanded fivefold by supplementing the dataset with DOTA and data augmentation techniques. Framework-wise, based on the Faster R-CNN model, the combination of a residual backbone network and pyramid balancing structure enables our model to adapt to the characteristics of small-target scenarios. Moreover, the attention mechanism, random anchor re-selection strategy, and the strategy of replacing quantization operations with bilinear interpolation further enhance the model’s detection capability at a low cost. Ablation experiments and comparative experiments show that, with a simple backbone, the algorithm in this paper achieves a mAP of 71.2% on the dataset, an improvement in accuracy of about 10% compared to the Faster R-CNN algorithm.

In this paper, we define the fuzzy set-valued homomorphisms of the canonical hypergroups as a generalization of fuzzy congruences and investigate some of their features. This structure is an extension of the definition of set-valued homomorphism defined for groups to hypergroups. With this extension, it has become possible to study generalized fuzzy rough approximations in hyperalgebraic structures such as semihypergroups, polygroups, hyperrings, hypermodules, etc. This paper presents the generalized fuzzy rough approximations based on two-universe (I,T)-fuzzy model on canonical hypergroups.

The rapid development of artificial intelligence (AI) and 5G paradigm brings infinite possibilities for data annotation for new applications in the industrial Internet of Things (IIoT). However, the problem of data annotation consistency under distributed architectures and growing concerns about issues such as data privacy and cybersecurity are major obstacles to improving the quality of distributed data annotation. In this paper, we propose a reputation-based asynchronous federated learning approach for digital twins. First, this paper integrates digital twins into an asynchronous federated learning framework, and utilizes a smart contract-based reputation mechanism to enhance the interconnection and internal interaction of asynchronous mobile terminals. In addition, in order to enhance security and privacy protection in the distributed smart annotation system, this paper introduces blockchain technology to optimize the data exchange, storage, and sharing process to improve system security and reliability. The data results show that the consistency of our proposed FedDTrep distributed intelligent labeling system reaches 99%.

In Mobile Crowdsensing (MCS), sensing tasks have different impacts and contributions to the whole system or specific targets, so the importance of the tasks is different. Since resources for performing tasks are usually limited, prioritizing the allocation of resources to more important tasks can ensure that key data or information can be collected promptly and accurately, thus improving overall efficiency and performance. Therefore, it is very important to consider the importance of tasks in the task selection and allocation of MCS. In this paper, a task queue is established, the importance of tasks, the ability of participants to perform tasks, and the stability of the task queue are considered, and a novel task selection and allocation scheme (TSAS) in the MCS system is designed. This scheme introduces the Lyapunov optimization method, which can be used to dynamically keep the task queue stable, balance the execution ability of participants and the system load, and perform more important tasks in different system states, even when the participants are limited. In addition, the Double Deep Q-Network (DDQN) method is introduced to improve on the traditional solution of the Lyapunov optimization problem, so this scheme has a certain predictive ability and foresight on the impact of future system states. This paper also proposes action-masking and iterative training methods for the MCS system, which can accelerate the training process of the neural network in the DDQN and improve the training effect. Experiments show that the TSAS based on the Lyapunov optimization method and DDQN performs better than other algorithms, considering the long-term stability of the queue, the number and importance of tasks to be executed, and the congestion degree of tasks.

With the emergence and development of application requirements such as data analysis and publishing, it is particularly important to use differential privacy protection technology to provide more reliable, secure, and compliant datasets for research in the field of children’s health. This paper focuses on the differential privacy protection of the ultrasound examination health dataset of adolescents in southern Texas from three aspects: differential privacy protection with output perturbation on basic statistics, publication of differential privacy marginal histogram and synthesized data, and a machine learning differential privacy learning algorithm. Firstly, differential privacy protection results with output perturbation show that Laplace and Gaussian mechanisms for numerical data, as well as the exponential mechanism for non-numerical data, can achieve the goal of protecting privacy. The exponential mechanism provides higher privacy protection. Secondly, a differential privacy marginal histogram with four attributes can be obtained with an appropriate privacy budget that approximates the marginal histogram of the original data. In order to publish synthetic data, we construct a synthetic query to obtain the corresponding differential privacy histogram for two attributes. Further, a synthetic dataset can be constructed by following the data distribution of the original dataset and the quality of the synthetic data publication can also be evaluated by the mean square error and error rate. Finally, consider a differential privacy logistic regression model under machine learning to predict whether children have fatty liver in binary classification tasks. The experimental results show that the model combined with quadratic perturbation has better accuracy and privacy protection. This paper can provide differential privacy protection models under different demands, which provides important data release and analysis options for data managers and research organizations, in addition to enriching the research on child health data releasing and mining.

In knowledge structure theory (KST), an individual’s knowledge state represents the items that the individual can completely solve. Based on the differences in individuals’ latent cognitive competence, polytomous knowledge states can be used to partially represent individuals to solve items. This paper explores the construction of polytomous knowledge states and polytomous knowledge structures on a polytomous knowledge domain Q×L. A quasi-ordinal polytomous knowledge space and a polytomous knowledge space can be induced by two different entail relations, respectively. When the polytomous knowledge structure (Q,L,K) on Q×L is determined, accurately evaluating an individual’s polytomous knowledge state is the key to providing learning guidance and taking teaching remedial measures for the individual. Therefore, we study the basic assessment procedure for a given polytomous knowledge structure, and a concrete example is designed to illustrate the method presented in this paper.

A System-of-Systems (SoS) is characterized both by independence and by inter-dependency. This inter-dependency, while allowing an SoS to achieve its objectives, also means that failures can cascade throughout the SoS. An SoS needs to be resilient to deal with the impact of complex internal and external environments. In this paper, we propose a resilience analysis method of an SoS based on a hierarchy structure. Firstly, we establish a hierarchy structure, which is ranked from high to low as capability level, activity level and system level. Then, Bayesian Networks (BNs) and Dynamic Bayesian Networks (DBNs) are used to analyze the resilience of the SoS. A resilience-based system importance metric is introduced, which is used in the budget allocation optimization problem during the development domain of an SoS. This paper proposes a mathematical programming model aimed at optimizing SoS resilience by optimally using budget to the subsystem. The application of the proposed approach is demonstrated using a case study: a Next Generation Air Transportation setting. The study results provide evidence that the proposed inter-dependency analysis based on Bayesian theory and the SoS resilience design approach can assist SoS system engineers in increasing expected SoS resilience during the development domain.

Most image quality assessment (IQA) algorithms based on sparse representation primarily focus on amplitude information, often overlooking the structural composition of images. However, structural composition is closely linked to perceived image quality, a connection that existing methods do not adequately address. To fill this gap, this paper proposes a novel distorted-image quality assessment algorithm based on a sparse structure and subjective perception (IQA-SSSP). This algorithm evaluates the quality of distorted images by measuring the sparse structure similarity between a reference and distorted images. The proposed method has several advantages. First, the sparse structure algorithm operates with reduced computational complexity, leading to faster processing speeds, which makes it suitable for practical applications. Additionally, it efficiently handles large-scale data, further enhancing the assessment process. Experimental results validate the effectiveness of the algorithm, showing that it achieves a high correlation with human visual perception, as reflected in both objective and subjective evaluations. Specifically, the algorithm yielded a Pearson correlation coefficient of 0.929 and a mean squared error of 8.003, demonstrating its robustness and efficiency. By addressing the limitations of existing IQA methods and introducing a more holistic approach, this paper offers new perspectives on IQA. The proposed algorithm not only provides reliable quality assessment results but also closely aligns with human visual experience, thereby enhancing both the objectivity and accuracy of image quality evaluations. This research offers significant theoretical support for the advancement of sparse representation in IQA.

This paper employs an integral reinforcement learning (IRL) method to investigate the optimal tracking control problem (OTCP) for nonlinear nonzero-sum (NZS) differential game systems with unknown drift dynamics. Unlike existing methods, which can only bound the tracking error, the proposed approach ensures that the tracking error asymptotically converges to zero. This study begins by constructing an augmented system using the tracking error and reference signal, transforming the original OTCP into solving the coupled Hamilton–Jacobi (HJ) equation of the augmented system. Because the HJ equation contains unknown drift dynamics and cannot be directly solved, the IRL method is utilized to convert the HJ equation into an equivalent equation without unknown drift dynamics. To solve this equation, a critic neural network (NN) is employed to approximate the complex value function based on the tracking error and reference information data. For the unknown NN weights, the least squares (LS) method is used to design an estimation law, and the convergence of the weight estimation error is subsequently proven. The approximate solution of optimal control converges to the Nash equilibrium, and the tracking error asymptotically converges to zero in the closed system. Finally, we validate the effectiveness of the proposed method in this paper based on MATLAB using the ode45 method and least squares method to execute Algorithm 2.

Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of introducing liquidity in portfolio optimization problems. For this purpose, first we consider three volume-based liquidity measures proposed in the literature and we build a new one particularly suited to portfolio optimization. Secondly, we formulate an extended version of the Markowitz portfolio selection problem, named mean–variance–liquidity, wherein the goal is to minimize the portfolio variance subject to the usual constraint on the expected portfolio return and an additional constraint on the portfolio liquidity. Thirdly, we consider a sensitivity analysis, with the aim to assess the trade-offs between liquidity and return, on the one hand, and between liquidity and risk, on the other hand. In the second part of the paper, the portfolio optimization framework is applied to a dataset of US ETFs comprising both standard and alternative, often illiquid, investments. The analysis is carried out with all the liquidity measures considered, allowing us to shed light on the relationships among risk, return and liquidity. Finally, we study the effects of the introduction of a Bitcoin ETF, as an asset with an extremely high expected return and risk.

In this paper, we propose a discrete Hamilton–Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton–Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton–Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton–Jacobi equation is related to the continuous Hamilton–Jacobi theory presented in this work. Then, we propose geometric foundations of the discrete Hamilton–Jacobi equations on contact manifolds in terms of discrete contact flows. At the end of the paper, we provide a numerical example to test the theory.

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given.