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This book collects under one cover twelve original research papers and one review paper submitted to the Special Issue “State-of-the-Art Mathematical Applications in Europe” and published in the MDPI journal Mathematics from December 2021 to January 2023 [...]

This paper studies the problem of adaptive fuzzy control based on command filtering for a class of nonlinear systems characterized by an input dead zone, input saturation, and unknown control direction. First, this paper proposes a novel equivalent transformation technique that simplifies the design complexity of multiple input constraints by converting the input dead zone and saturation nonlinearities into a unified functional form. Subsequently, a fuzzy logic system is utilized to handle the unknown nonlinear functions, and the command-filtering method is employed to address the issue of complexity explosion, while the Nussbaum function is utilized to resolve the challenge of an unknown control direction. Based on Lyapunov stability, it is proven that the tracking error converges to a small neighborhood around the origin, and all closed-loop signals are bounded. Finally, a numerical simulation result and an actual simulation result of a pendulum are presented to verify the feasibility and effectiveness of the proposed control strategy.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but as shown in this paper, it does not admit solutions where the receiver is allowed to move. To overcome this limitation, a new wave equation that permits both the receiver and the source to move is derived in this paper. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by a stationary point source. From this purely mathematical definition, the wave equation for a stationary source and a moving receiver is derived, together with a corresponding free-space Green function. Utilizing the derived Green function, it is shown that unlike the standard wave equation this new wave equation also permits solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for a moving source and a moving receiver governs the waves emitted by moving point sources and received by moving receivers. This new wave equation has possible applications in acoustics, electrodynamics, and other physical sciences.

The warning of the potential faults occurring in the future in a sucker rod well can help technicians adjust production strategies in time. It is of great significance for safety during well production. In this paper, the key characteristic parameters of dynamometer cards were predicted by a temporal neural network to implement the warning of different working conditions which might result in failures. First, a one-dimensional damped-wave equation was used to eliminate the dynamic loads’ effect of surface dynamometer cards by converting them into down-hole dynamometer cards. Based on the down-hole dynamometer cards, the characteristic parameters were extracted, including the load change, the position of the valve opening and closing point, the dynamometer card area, and so on. The mapping relationship between the characteristic parameters and working conditions (classification model) was obtained by the Xgboost algorithm. Meanwhile, the noise in these parameters was reduced by wavelet transformation, and the rationality of the results was verified. Second, the Encoder–Decoder and multi-head attention structures were used to set up the time series prediction model. Then, the characteristic parameters were predicted in a sequence-to-sequence way by using historical characteristic parameters, date, and pumping parameters as input. At last, by inputting the predicted results into the classification model, a working conditions warning method was created. The results showed that noise reduction improved the prediction accuracy significantly. The prediction relative error of most characteristic parameters was less than 15% after noise reduction. In most working conditions, their F1 values were more than 85%. Most Recall values could be restored to over 90% of those calculated by real parameters, indicating few false negative cases. In general, the warning method proposed in this paper can predict faulty working conditions that may occur in the future in a timely manner.

In this paper, we develop a new Best Uniform Rational Approximation-Semi-Discrete (BURA-SD) method taking into account the singularities of the solution of fractional diffusion problems in polygonal domains. The complementary capabilities of the exponential convergence rate of BURA-SD and the hp FEM are explored with the aim of maximizing the overall performance. A challenge here is the emerging singularly perturbed diffusion–reaction equations. The main contributions of this paper include asymptotically accurate error estimates, ending with sufficient conditions to balance errors of different origins, thereby guaranteeing the high computational efficiency of the method.

Learning linear and nonlinear dynamical systems from available data is a timely topic in scientific machine learning. Learning must be performed while enforcing the numerical stability of the learned model, the existing knowledge within an informed or augmented setting, or by taking into account the multiscale dynamics—for both linear and nonlinear dynamics. However, when the final objective of such a learned dynamical system is to be used for control purposes, learning transformed dynamics can be advantageous. Therefore, many alternatives exists, and the present paper focuses on two of them: the first based on the discovery and use of the so-called flat control and the second one based on the use of the Koopman theory. The main contributions when addressing the first is the discovery of the flat output transformation by using an original neural framework. Moreover, when using the Koopman theory, this paper proposes an original procedure for learning parametric dynamics in the latent space, which is of particular interest in control-based engineering applications.

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied by using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results.

Prefabricated cabin modular units (PMCUs) are a widespread type of intermediate products used during ship or offshore platform construction. This paper focuses on the scheduling problem of PMCU assembly flow shops, which is summarized as a multi-objective, fuzzy-blocking hybrid flow-shop-scheduling problem based on learning and fatigue effects (FB-HFSP-LF) to minimize the maximum fuzzy makespan and maximize the average fuzzy due-date agreement index. This paper proposes a multi-objective non-dominated sorting gravitational search algorithm (MONSGSA) to solve it. In the proposed MONSGSA, the ranked-order value is used to convert continuous solutions to discrete solutions. Multi-dimensional Latin hypercube sampling is used to enhance initial population diversity. Setting up an external archive to maintain non-dominated solutions while introducing an adaptive inertia factor and a trap avoidance operator to guide individual positional updates. The results of multiple sets of experiments show that Pareto solutions of MONSGSA have better distribution and convergence compared to other competitors. Finally, the instance of PMCU manufacturer is used for validation, and the results show that MONSGSA has better applicability to practical problems.

Predicting student performance in the future is a crucial behavior prediction problem in education. By predicting student performance, educational experts can provide individualized instruction, optimize the allocation of resources, and develop educational strategies. If the prediction results are unreliable, it is difficult to earn the trust of educational experts. Therefore, prediction methods need to satisfy the requirement of interpretability. For this reason, the prediction model is constructed in this paper using belief rule base (BRB). BRB not only combines expert knowledge, but also has good interpretability. There are two problems in applying BRB to student performance prediction: first, in the modeling process, the system is too complex due to the large number of indicators involved. Secondly, the interpretability of the model can be compromised during the optimization process. To overcome these challenges, this paper introduces a hierarchical belief rule base with interpretability (HBRB-I) for student performance prediction. First, it analyzes how the HBRB-I model achieves interpretability. Then, an attribute grouping method is proposed to construct a hierarchical structure by reasonably organizing the indicators, so as to effectively reduce the complexity of the model. Finally, an objective function considering interpretability is designed and the projected covariance matrix adaptive evolution strategy (P-CMA-ES) optimization algorithm is improved. The aim is to ensure that the model remains interpretable after optimization. By conducting experiments on the student performance dataset, it is demonstrated that the proposed model performs well in terms of both accuracy and interpretability.

The achievable capacity index (ACI) is a simple and efficient approach for estimating the profitability of newsboy-type products, wherein profitability is defined as the probability of achieving the target profit by optimizing the order quantity. At present, the ACI is applicable to single retail stores (i.e., single demand) but not to multiple sales channels (i.e., multiple demand). This paper presents an integrated achievable capacity index (IACI) by which to measure the aggregate profitability of multiple mutually independent channels under normally distributed demand. An unbiased IACI estimator is also developed, to which is applied the Taylor expansion to approximate its sampling distribution, wherein the sizes, means, and variances of demand differ in each channel. Furthermore, overestimates due to sampling error are avoided by deriving the lower confidence bound for the IACI. This paper also provides generic tables to aid managers seeking conservative estimates of profitability. The applicability of the proposed scheme is demonstrated numerically using a real-world example involving an own-branding-and-manufacturing (OBM) enterprise with multiple owned channels.

This paper introduces a novel error-based adaptive feedback zeroing neural network (EAF-ZNN) to solve the time-varying quadratic programming (TVQP) problem. Compared to existing variable gain ZNNs, the EAF-ZNN dynamically adjusts the parameter to adaptively accelerate without increasing to very large values over time. Unlike adaptive fuzzy ZNN, which only considers the current convergence error, EAF-ZNN ensures regulation by introducing a feedback regulation mechanism between the current convergence error, the historical cumulative convergence error, the change rate of the convergence error, and the model gain parameter. This regulation mechanism promotes effective neural dynamic evolution, which results in high convergence rate and accuracy. This paper provides a detailed analysis of the convergence of the model, utilizing four distinct activation functions. Furthermore, the effect of changes in the proportional, integral, and derivative factors in the EAF-ZNN model on the rate of convergence is explored. To assess the superiority of EAF-ZNN in solving TVQP problems, a comparative evaluation with three existing ZNN models is performed. Simulation experiments demonstrate that the EAF-ZNN model exhibits a superior convergence rate. Finally, the EAF-ZNN model is compared with the other three models through the redundant robotic arms example, which achieves smaller position error.

In this paper, we examine a sequence of uncountable iterated function systems (U.I.F.S.), where each term in the sequence is constructed from an uncountable collection of contraction mappings along with a linear and continuous operator. Each U.I.F.S. within the sequence is associated with an attractor, which represents a set towards which the system evolves over time, a Markov-type operator that governs the probabilistic behavior of the system, and a fractal measure that describes the geometric and measure-theoretic properties of the attractor. Our study is centered on analyzing the convergence properties of these systems. Specifically, we investigate how the attractors and fractal measures of successive U.I.F.S. in the sequence approach their respective limits. By understanding the convergence behavior, we aim to provide insights into the stability and long-term behavior of such complex systems. This study contributes to the broader field of dynamical systems and fractal geometry by offering new perspectives on how uncountable iterated function systems evolve and stabilize. In this paper, we undertake a comprehensive examination of a sequence of uncountable iterated function systems (U.I.F.S.), each constructed from an uncountable collection of contraction mappings in conjunction with a linear and continuous operator. These systems are integral to our study as they encapsulate complex dynamical behaviors through their association with attractors, which represent sets towards which the system evolves over time. Each U.I.F.S. within the sequence is governed by a Markov-type operator that dictates its probabilistic behavior and is described by a fractal measure that captures the geometric and measure-theoretic properties of the attractor. The core contributions of our work are presented in the form of several theorems. These theorems tackle key problems and provide novel insights into the study of measures and their properties in Hilbert spaces. The results contribute to advancing the understanding of convergence behaviors, the interaction of Dirac measures, and the applications of Monge–Kantorovich norms. These theorems hold significant potential applications across various domains of functional analysis and measure theory. By establishing new results and proving critical properties, our work extends existing frameworks and opens new avenues for future research. This paper contributes to the broader field of mathematical analysis by offering new perspectives on how uncountable iterated function systems evolve and stabilize. Our findings provide a foundational understanding that can be applied to a wide range of mathematical and real-world problems. By highlighting the interplay between measure theory and functional analysis, our work paves the way for further exploration and discovery in these areas, thereby enriching the theoretical landscape and practical applications of these mathematical concepts.

The vehicle–guideway coupled self-excited vibration of maglev systems is a common control instability problem in maglev traffic while the train is suspended above flexible girders, and it seriously affects the suspension stability of maglev vehicles. In order to solve this problem, a nonlinear dynamic model of a single-point maglev system with elastic track is established in this paper, and a new and more stable adaptive backstepping control method combined with magnetic flux feedback is designed. In order to verify the control effect of the designed control method, a maglev vehicle–guideway coupled experimental platform with elastic track is built, and experimental verifications under rigid and elastic conditions are carried out. The results show that, compared with the state feedback controller based on the feedback linearization controller, the adaptive backstepping control law proposed in this paper can achieve stable suspension under extremely low track stiffness, and that it shows good stability and anti-interference abilities under elastic conditions. This work has an important meaning regarding its potential to benefit the advancement of commercial maglev lines, which may significantly enhance the stability of the maglev system and reduce the cost of guideway construction.

This paper introduces an autonomous robot designed for in-pipe structural health monitoring of oil/gas pipelines. This system employs a 3D Optical Laser Scanning Technical Vision System (TVS) to continuously scan the internal surface of the pipeline. This paper elaborates on the mathematical methodology of 3D laser surface scanning based on dynamic triangulation. This paper presents the mathematical framework governing the combined kinematics of the Mobile Robot (MR) and TVS. It discusses the custom design of the MR, adjusting it to use of robustized mathematics, and incorporating a laser scanner produced using a 3D printer. Both experimental and theoretical approaches are utilized to illustrate the formation of point clouds during surface scanning. This paper details the application of the simple and robust mathematical algorithm RANSAC for the preliminary processing of the measured point clouds. Furthermore, it contributes two distinct and simplified criteria for detecting defects in pipelines, specifically tailored for computer processing. In conclusion, this paper assesses the effectiveness of the proposed mathematical and physical method through experimental tests conducted under varying light conditions.

Coal mining under the Quaternary thick loose layer affects key strata breakage, Bed-separations development, ground subsidence, and other studies. This paper presents a method for solving the deflection of a large-deflection inclined thin plate under a thick loose-layer cover with additional lateral loads and midplane forces. The methods presented are based on the principle of large-deflection of thin-plate, energy method, and fracture mechanics theory. The 7225 work face in Anhui Province, China, was studied. Combined with the large-deflection inclined thin plate model, the initial breakage distance within the main roof plate was calculated to be 33 m with the initial breakage angle of 61.2°, and the period breakage distance was calculated to be 21 m with the period breakage angle of 55.4°. The distribution range of “Vertical Three Zones” from 7225 working face to the ground, including the height of the caved zone is 38.07 m, the height of the fractured zone is 41.13 m, and the height of the curved zone with the thick loose layer removed is 187.56 m. During the dynamic development of the principal key strata (PKS), the deflection value develops from 0 mm to 2714 mm with 7225 working face mining, and the maximum value of the spatial volume is 56,485 m3, which is verified by Three-dimensional Discrete Element Code (3DEC) numerical simulation. The dynamic development of Bed-separation within the overlying strata, with a maximum development height of 545.2 mm and a maximum volume of 11,228.1 m3 of the Bed-separation cavity. The dynamic development of the Bed-separation height and the cavity under different mining length and width conditions of the working face are also discussed. The large-deflection inclined thin plate model proposed in this paper effectively explores the dynamic deflection and fragmentation law of the overlying strata induced by the inclined working face of Longwall mining and provides a theoretical basis and computational model for quantitatively evaluating the dynamic development of the Bed-separation cavity.

Adjusting the energy structure of various industries is crucial for achieving China’s carbon peak and carbon neutrality goals. Given the significant proportion of carbon emissions from the logistics industry in the tertiary sector, the research on predicting the carbon emissions of the logistics industry is of great significance for China to achieve its “Dual carbon” target. In this paper, the gray relational analysis (GRA) methodology is adopted to screen the influencing factors of carbon emissions in the logistics industry firstly. Then, the particle swarm optimization (PSO) algorithm was used to optimize the penalty coefficientand kernel function range parameter of the support vector regression (SVR) model (i.e. PSO- SVR model). The data from 2000 to 2021 regarding carbon emissions and related influencing factors in China’s logistics industry are analyzed, and the mean absolute percentage error (MAPE) of the PSO-SVR model is 0.82%, which shows that the proposed PSO-SVR model in this paper is effective. Finally, instructive suggestions are provided for China to achieve the “Dual Carbon” goal and upgrading of the logistics industry.

With the occurrence of the global financial crisis in 2008, the U.S. unconventional monetary policy affected the Chinese market. Based on a monthly data sample from 2008M1 to 2015M12, in this paper we identify U.S. and Chinese monetary policy shocks by using a structural vector autoregression (SVAR) model with multi-external instrumental variables along with principal component analysis (PCA) combined with high-frequency financial market data. The empirical results show that the unconventional monetary policies had a negative effect on China’s inflation and output due to the signal effect, and China’s stock and commodity markets increased in the short term. During the same period, China’s monetary policy had a greater impact on the domestic economy and financial markets. The conclusion of this paper provides a significant reference for relevant departments to make decisions amidst the new wave of unconventional U.S. monetary policies due to the COVID-19 pandemic.

The complexity, increasing flow number and volumes, and challenges of last-mile logistics (LML) motivate or compel companies, authorities, and the entire community to think about ways to increase efficiency, reliability, and profits, reduce costs, reduce negative environmental impacts, etc. These objectives can be met by applying Industry 4.0 (I4.0) technologies, but the key question is which one. To solve this task, this paper used an innovative method that combines the fuzzy analytic network process (fuzzy ANP) and the fuzzy axial-distance-based aggregated measurement (fuzzy ADAM) method. The first was used for determining criteria weights and the second for selecting the best variant. The best solution is e/m-marketplaces, followed by cloud-computing-supported management and control systems and blockchain. These results indicate that widely adopted and implemented technologies are suitable for last-mile logistics. Newer technologies already producing significant results have serious potential for further development in this area. The main novelties and contributions of this paper are the definition of a new methodology based on multi-criteria decision-making (MCDM) methods, as well as its application for ranking I4.0 technologies for LML.

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these.

The geological complexity, environmental sensitivity, and ecological fragility inherent in complex and difficult areas (CDAs) present new opportunities and challenges for technological innovation in railway engineering development in China. At the current stage in China, the process of technological innovation in railway engineering within CDAs still faces a series of pressing issues that need addressing. The paper identifies and determines 22 influencing factors for technological innovation in railway engineering within CDAs across five dimensions. Subsequently, a technological innovation model for railway engineering in such areas is constructed based on system dynamics (SD), which is followed by simulation and sensitivity analysis to identify the key influencing factors. The results indicate that key influencing factors for technological innovation in railway engineering within CDAs include technological innovation capability, the adaptability of technology to the environment, R&D funding investment, technological product requirements, technological innovation incentive mechanisms, and the level of technological development. The importance ranking of each dimension is as follows: technological factors > technical factors > management factors > resource factors > environmental factors. The paper provides new insights for promoting technological innovation and management development in complex and challenging railway engineering projects. It offers a fresh perspective to enhance the technological innovation efficiency of railway projects in complex and challenging areas.

A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the local problem. At the end, we present a particularization of the local and nonlocal problems, with applications for image processing (reconstruction, segmentation, etc.). Some conclusions are given, as well as new directions to extend the results and methods presented in this paper.

The question of whether there is a true isometry that approximates the ε-isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, the authors published some papers improving the previous results. The main purpose of this paper is to improve all of the abovementioned results by utilizing the properties of the norm and inner product for Euclidean space.

Geary’s c is a prominent measure of spatial autocorrelation in univariate spatial data. It uses a weighted sum of squared differences. This paper develops Geary’s c for multivariate spatial data. It can describe the similarity/discrepancy between vectors of observations at different vertices/spatial units by a weighted sum of the squared Euclidean norm of the vector differences. It is thus a natural extension of the univariate Geary’s c. This paper also develops a local version of it. We then establish their properties.

The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper, we face the modular quasi-(pseudo-)metric aggregation problem, which consists of analyzing the properties that a function must have to fuse a collection of modular quasi-(pseudo-)metrics into a single one. In this paper, we characterize such functions as monotone, subadditive and vanishing at zero. Moreover, a description of such functions in terms of triangle triplets is given, and, in addition, the relationship between modular quasi-(pseudo-)metric aggregation functions and modular (pseudo-)metric aggregation functions is discussed. Specifically, we show that the class of modular (quasi-)(pseudo-)metric aggregation functions coincides with that of modular (pseudo-)metric aggregation functions. The characterizations are illustrated with appropriate examples. A few methods to construct modular quasi-(pseudo-)metrics are provided using the exposed theory. By exploring the existence of absorbent and neutral elements of modular quasi-(pseudo-)metric aggregation functions, we find that every modular quasi-pseudo-metric aggregation function with 0 as the neutral element is an Aumann function, is majored by the sum and satisfies the 1-Lipschitz condition. Moreover, a characterization of those modular quasi-(pseudo-)metric aggregation functions that preserve modular quasi-(pseudo-)metrics is also provided. Furthermore, the relationship between modular quasi-(pseudo-)metric aggregation functions and quasi-(pseudo-)metric aggregation functions is studied. Particularly, we have proven that they are the same only when the former functions are finite. Finally, the usefulness of modular quasi-(pseudo-)metric aggregation functions in multi-agent systems is analyzed.

In order to fulfill the practical application demands of precisely localizing underwater vehicles using passive electric field localization technology, we propose a scalar-potential-based method for the passive electric field localization of underwater vehicles. This method is grounded on an intelligent differential evolution algorithm and is particularly suited for use in three-layer and stratified oceanic environments. Firstly, based on the potential distribution law of constant current elements in a three-layer parallel stratified ocean environment, the mathematical positioning model is established using the mirror method. Secondly, the differential evolution (DE) algorithm is enhanced with a parameter-adaptive strategy and a boundary mutation processing mechanism to optimize the key objective function in the positioning problem. Additionally, the simulation experiments of the current element in the layered model prove the effectiveness of the proposed positioning method and show that it has no special requirements for the sensor measurement array, but the large range and moderate number of sensors are beneficial to improve the positioning effect. Finally, the laboratory experiments on the positioning method proposed in this paper, involving underwater simulated current elements and underwater vehicle tracks, were carried out successfully. The results indicate that the positioning method proposed in this paper can achieve the performance requirements of independent initial value, strong anti-noise capabilities, rapid positioning speed, easy implementation, and suitability in shallow sea environments. These findings suggest a promising practical application potential for the proposed method.

This paper is devoted to the study of the multi-dimensional integral transform with the Fox H-function in the kernel in weighted spaces with integrable functions in the domain R+n with positive coordinates. Due to the generality of the Fox H-function, many special integral transforms have the form studied in this paper, including operators with such kernels as generalized hypergeometric functions, classical hypergeometric functions, Bessel and modified Bessel functions and so on. Moreover, most important fractional integral operators, such as the Riemann–Liouville type, are covered by the class under consideration. The mapping properties in Lebesgue-weighted spaces, such as the boundedness, the range and the representations of the considered transformation, are established. In special cases, it is applied to the specific integral transforms mentioned above. We use a modern technique based on the extensive use of the Mellin transform and its properties. Moreover, we generalize our own previous results from the one-dimensional case to the multi-dimensional one. The multi-dimensional case is more complex and needs more delicate techniques.

This paper investigates the problem of the adaptive neural network tracking control of nonlinear cyber–physical systems (CPSs) subject to unknown deception attacks with prescribed performance. The considered system is under the influence of unknown deception attacks on both actuator and sensor networks, making the research problem challenging. The outstanding contribution of this paper is that a new anti-deception attack-prescribed performance tracking control scheme is proposed through a special coordinate transformation and funnel function, combined with backstepping and bounded estimation methods. The transient performance of the system can be ensured by the prescribed performance control scheme, which makes the indicators of the controlled system, such as settling time and tracking accuracy, able to be pre-assigned offline according to the task needs, and the applicability of the prescribed performance is tested by selecting different values of the settling time (0.5 s, 1 s, 1.5 s, 2 s, 2.5 s, and 3 s). In addition, to save the computational and communication resources of the CPS, this paper uses a finite-time differentiator to approximate the virtual control law differentiation to avoid “complexity explosion” and a switching threshold event triggering mechanism to save the communication resources for data transmission. Finally, the effectiveness of the proposed control strategy is further verified by an electromechanical system simulation example.

In order to reduce pollution caused by ship emissions, the International Maritime Organization (IMO) implemented sulfur emission control areas (SECAs). In comparison to ordinary vessels, cruise ships with dual attributes of transportation and tourism generate a greater amount of marine pollution, which poses a significant threat to the marine environment in both berthing ports and the sailing area. In light of the fierce competition of the cruise tourism market, cruise lines are looking for strategies, such as designing more attractive cruise routes, to maintain their core competencies under the emission control policy. In order to achieve this goal, this paper presents a mixed-integer non-linear programming (MINP) model with two objectives and is derived from the traditional route optimization problem. The primary objective is to optimize the route and speed of a cruise liner, while simultaneously enhancing route competitiveness and minimizing carbon emissions both within and outside the SECAs. Subsequently, the multi-objective particle swarm optimization (MOPSO) algorithm was used to reach the objective, and simulations were carried out to verify the effectiveness of the model and method. The results show that speed and sailing route optimization can affect carbon emissions. This paper has a certain application value and guiding significance for cruise line decision makers that will be beneficial for the environment.

Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty and nonlinearity, making the construction of a robust and reliable forecasting model still a challenging task. Aiming at this nonlinear and complex traffic flow forecasting problem, this paper constructs a short-term traffic flow forecasting hybrid optimization model, SSA-ELM, based on extreme learning machine by embedding the sparrow search algorithm in order to solve the above problem. Extreme learning machine has been widely used in short-term traffic flow forecasting due to its characteristics such as low computational complexity and fast learning speed. By using the sparrow search algorithm to optimize the input weight values and hidden layer deviations in the extreme learning machine, the sparrow search algorithm is utilized to search for the global optimal solution while taking into account the original characteristics of the extreme learning machine, so that the model improves stability while increasing prediction accuracy. Experimental results on the Amsterdam A10 road traffic flow dataset show that the traffic flow forecasting model proposed in this paper has higher forecasting accuracy and stability, revealing the potential of hybrid optimization models in the field of short-term traffic flow forecasting.

In this paper, we collect the basic information data of online rumors and highly topical public opinions. In the research of the propagation model of online public opinion rumors, we use the improved SCIR model to analyze the characteristics of online rumor propagation under the suspicion mechanism at different propagation stages, based on considering the flow of rumor propagation. We analyze the stability of the evolution of rumor propagation by using the time-delay differential equation under the punishment mechanism. In this paper, the evolution of heterogeneous views with different acceptance and exchange thresholds is studied, using the standard Deffuant model and the improved model under the influence of the media, to analyze the evolution process and characteristics of rumor opinions. Based on the above results, it is found that improving the recovery rate is better than reducing the deception rate, and increasing the eviction rate is better than improving the detection rate. When the time lag τ < 110, it indicates that the spread of rumors tends to be asymptotic and stable, and the punishment mechanism can reduce the propagation time and the maximum proportion of deceived people. The proportion of deceived people increases with the decrease in the exchange threshold, and the range of opinion clusters increases with the decline in acceptance.

In this paper, we consider and study in detail the generalized Fox–Wright function Ψ˜qp introduced in our recent work as an extension of the Fox–Wright function Ψqp. This special function can be seen as an important case of the so-called I-functions of Rathie and H¯-functions of Inayat-Hussain, that in turn extend the Fox H-functions and appear to include some Feynman integrals in statistical physics, in polylogarithms, in Riemann Zeta-type functions and in other important mathematical functions. Depending on the parameters, Ψ˜qp is an entire function or is analytic in an open disc with a final radius. We derive its basic properties, such as its order and type, and its images under the Laplace transform and under classical fractional-order integrals. Particular cases of Ψ˜qp are specified, including the Mittag-Leffler and Le Roy-type functions and their multi-index analogues and many other special functions of Fractional Calculus. The corresponding results are illustrated. Finally, we emphasize the role of these new generalized hypergeometric functions as eigenfunctions of operators of new Fractional Calculus with specific I-functions as singular kernels. This paper can be considered as a natural supplement to our previous surveys “Going Next after ‘A Guide to Special Functions in Fractional Calculus’: A Discussion Survey”, and “A Guide to Special Functions of Fractional Calculus”, published recently in this journal.

This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the original boundary value problem. The model under consideration consists of the Navier–Stokes equations, the Maxwell equations without displacement currents, the generalized Ohm’s law for a moving medium and the convection-diffusion equation for temperature. These relations are nonlinearly connected via the Lorentz force, buoyancy force in the Boussinesq approximation and convective heat transfer. Results concerning the existence and uniqueness of the solution of the original boundary value problem and of its generalized linear analog are presented. The global solvability of the control problem under study is proved and the optimality system is derived. Sufficient conditions on the data are established which ensure local uniqueness and stability of solutions of the control problems under study with respect to small perturbations of the cost functional to be minimized and one of the given functions. We stress that the unique stability estimates obtained in the paper have a clear mathematical structure and intrinsic beauty.

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results.

The main objective of this paper is to reduce the dimensionality of unknown coefficient vectors of finite-element (FE) solutions in two-grid (CN) FE (TGCNFE) format for the nonlinear unsaturated soil water flow problem by using a proper orthogonal decomposition (POD) and to design a new reduced-dimension iteration TGCNFE (RDITGCNFE). For this objective, a new time semi-discrete CN (TSDCN) scheme for the nonlinear unsaturated soil water flow problem is first designed and the existence, stability, and error estimates of TSDCN solutions are demonstrated. Subsequently, a new TGCNFE format for the nonlinear unsaturated soil water flow problem is designed and the existence, unconditional stability, and error estimates of TGCNFE solutions are demonstrated. Next, a new RDITGCNFE format with the same FE basis functions as the TGCNFE format is built by the POD method and the existence, unconditional stability, and error estimates of RDITGCNFE solutions are discussed. Ultimately, the rightness of theory results and the superiority of the RDITGCNFE format are verified by two sets of numerical tests. It is worth noting that the RDITGCNFE format differs completely from all previous reduced-dimension methods, including the authors’ previous works. Therefore, the study of this paper can not only provide a new theoretical method for the dimensionality reduction of numerical models for nonlinear problems but also provide an algorithm implementation technology for the numerical simulation of practical engineering problems.

Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introduced to cope with the local imprecision of the feature maps. However, in fuzzy set theory, it is not always accurate to assume that the degree of non-membership of an element in a fuzzy set is simply the complement of the degree of membership. This is due to the potential existence of a hesitation degree, which implies a certain level of uncertainty. To overcome this limitation, intuitionistic fuzzy sets (IFS) were introduced to incorporate the concept of a degree of hesitation. In this paper, we introduce a novel pooling operation based on intuitionistic fuzzy sets to incorporate the degree of hesitation heretofore neglected by a fuzzy pooling operation based on classical fuzzy sets, and we investigate its performance in the context of image classification. Intuitionistic pooling is performed in four steps: bifuzzification (by the transformation of data through the use of membership and non-membership maps), first aggregation (through the transformation of the IFS into a standard fuzzy set, second aggregation (through the transformation and use of a sum operator), and the defuzzification of feature map neighborhoods by using a max operator. IFS pooling is used for the construction of an intuitionistic pooling layer that can be applied as a drop-in replacement for the current, fuzzy (type-1) and crisp, pooling layers of CNN architectures. Various experiments involving multiple datasets demonstrate that an IFS-based pooling can enhance the classification performance of a CNN. A benchmarking study reveals that this significantly outperforms even the most recent pooling models, especially in stochastic environments.

Predicting breakthrough papers holds great significance; however, prior studies encountered challenges in this task, indicating a need for substantial improvement. We propose that the failure to capture the dynamic structural-evolutionary features of citation networks is one of the major reasons. To overcome this limitation, this paper introduces a new method for constructing citation cascades of focus papers, allowing the creation of a time-series-like set of citation cascades. Then, through a thorough review, three types of structural indicators in these citation networks that could reflect breakthroughs are identified, including certain basic topological metrics, PageRank values, and the von Neumann graph entropy. Based on the time-series-like set of citation cascades, the dynamic trajectories of these indicators are calculated and employed as predictors. Using the Nobel Prize-winning papers as a landmark dataset, our prediction method yields approximately a 7% improvement in the ROC-AUC score compared to static-based prior methods. Additionally, our method advances in achieving earlier predictions than other previous methods. The main contribution of this paper is proposing a novel method for creating citation cascades in chronological order and confirming the significance of predicting breakthroughs from a dynamic structural perspective.

This paper explores the integrated optimization of complex coupled industrial manufacturing systems and production strategies based on user customization needs. Two optimization metrics are considered: one is whether the production process of engineering manufacturing is simplified, and the other is whether it is based on the customization requirements of the customer. These two metrics are interrelated, and cases may even be conflicting. Considering the interdependence between engineering manufacturing and user requirements, this paper develops an integrated customized modular engineering manufacturing process to minimize production and maintenance costs and improve efficiency while meeting user customization requirements. This paper takes expert evaluation as an important decision indicator and optimizes the production process strategy on this basis. Finally, a case study is given to illustrate the applicability of the proposed process model.

Large-scale particle swarm optimization (PSO) has long been a hot topic due to the following reasons: Swarm diversity preservation is still challenging for current PSO variants for large-scale optimization problems, resulting in difficulties for PSO in balancing its exploration and exploitation. Furthermore, current PSO variants for large-scale optimization problems often introduce additional operators to improve their ability in diversity preservation, leading to increased algorithm complexity. To address these issues, this paper proposes a dual-competition-based particle update strategy (DCS), which selects the particles to be updated and corresponding exemplars with two rounds of random pairing competitions, which can straightforwardly benefit swarm diversity preservation. Furthermore, DCS confirms the primary and secondary exemplars based on the fitness sorting operation for exploitation and exploration, respectively, leading to a dual-competition-based swarm optimizer. Thanks to the proposed DCS, on the one hand, the proposed algorithm is able to protect more than half of the particles from being updated to benefit diversity preservation at the swarm level. On the other hand, DCS provides an efficient exploration and exploitation exemplar selection mechanism, which is beneficial for balancing exploration and exploitation at the particle update level. Additionally, this paper analyzes the stability conditions and computational complexity of the proposed algorithm. In the experimental section, based on seven state-of-the-art algorithms and a recently proposed large-scale benchmark suite, this paper verifies the competitiveness of the proposed algorithm in large-scale optimization problems.

The rapid development of supply chain finance (SCF) has significantly alleviated the financing difficulties of small and medium-sized enterprises (SMEs). However, it is important to recognize that within the accounts receivable financing segment of the SCF credit market, the credit risk associated with SMEs poses a serious challenge and potential threat to the stability, health, and sustainable development of the SCF system. This paper pays special attention to the stability of the two-party evolutionary game between SMEs and financial institutions (FIs) within the context of the Chinese SCF credit market. To identify a pathway to reduce credit risks for SMEs while simultaneously enhancing system stability, this paper adopts the stochastic evolutionary game (SEG) model and combines the fixed-point method to determine the conditions that satisfy the stability of the system’s index p mean square of the system. This study has made attempts in various aspects, such as the innovative construction and investigation of a nonlinear SEG model, the endeavor to study the stability of SEG systems using fixed-point methods, and the innovative construction of a more realistic two-player SEG system. The data and simulation results generated from hypothetical scenarios show that the conclusions of the article are credible and feasible. Through the study, we conclude that the higher credit ratio from FI and the higher penalty intensity from core enterprises (CEs) will accelerate the stability of the system. Based on solid data and modeling analysis, insights into the regulation of FI are provided.

In order to enhance the trajectory tracking accuracy of distributed-driven intelligent vehicles, this paper formulates the tasks of torque output control for longitudinal dynamics and steering angle output control for lateral dynamics as Markov decision processes. To dissect the requirements of action output continuity for longitudinal and lateral control, this paper adopts the deep deterministic policy gradient algorithm (DDPG) for longitudinal velocity control and the deep Q-network algorithm (DQN) for lateral motion control. Multi-agent reinforcement learning methods are applied to the task of trajectory tracking in distributed-driven vehicle autonomous driving. By contrasting with two classical trajectory tracking control methods, the proposed approach in this paper is validated to exhibit superior trajectory tracking performance, ensuring that both longitudinal velocity deviation and lateral position deviation of the vehicle remain at lower levels. Compared with classical control methods, the maximum lateral position deviation is improved by up to 90.5% and the maximum longitudinal velocity deviation is improved by up to 97%. Furthermore, it demonstrates excellent generalization and high computational efficiency, and the running time can be reduced by up to 93.7%.

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.

This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and monotonically decreasing delay intervals, respectively. Based on the constructed augmented Lyapunov functionals and the employed time-varying zero equation, less conservative stability criteria are obtained separately for bounded and periodic time-varying delays. Lastly, three examples are used to verify the superiority of the stability conditions obtained in this paper.

This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure was designed for the different demand scenarios, which allows comparison of the proposed approach with classical and fuzzy multi-item newsvendor problems; a modified genetic algorithm (GA) is introduced to ameliorate previous genetic algorithms in both the generation and evaluation of solutions. The new formulation of the fuzzy newsvendor problem, together with the modified GA, were shown to improve the average profit by up to 55% in problems with low-budget scenarios.

The issues of the evaluation and prediction of the reliability and testability of mining machinery and equipment are becoming particularly relevant, since the safety of technological processes and human life is reaching a new level of realisation due to changes in mining technology. The work is devoted to the development of a logical model for analysing the controllability of mining equipment. The paper presents a model of reliability of the operation of mining equipment on the example of a mine load and passenger hoist. This generalised model is made in the form of a graph of transitions and supplemented with a system of equations. The model allows for the estimation of the reliability of equipment elements and equipment as a whole. A mathematical and logical model for the calculation of the availability and downtime coefficients of various designs of mining equipment systems is proposed. This model became the basis for the methods to calculate the optimal values of diagnostic depth. At these calculated values, the maximum value of availability factor will be obtained. In this paper, an analytical study was carried out and dependences of the readiness factor of parameters of the investigated system such as the intensity of control of technical systems, intensity of failures, etc., were constructed. The paper proposes a mathematical model to assess the reliability of mine hoisting plants through its integration into the method of improving the reliability of mine hoisting plants.

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product based on adherence to a standard. Meanwhile, prior information, such as the process capability index (PCI), has been applied in different manufacturing industries to improve the quality of manufacturing processes and the quality inspection of products. In this paper, an attribute sampling plan is developed for submitted lots based on prior information and Bayesian approach. The new attribute sampling plans adjust sample sizes to prior information based on the status of the inspection target. To be specific, the sampling plans in this paper are indexed by the parameter trust with levels of low, medium, and high, where increasing trust level reduces sample size or risk. PCIs are an important basis for the choice of the trust level. In addition, multiple comparisons have been performed, including producer’s risk and consumer’s risk under different prior information parameters and different sample sizes.

Health status detection for motor drive systems includes detecting the working status of the motor and diagnosing open-circuit (OC) faults in the inverter. This paper proposes a generalized-layer-added principle component analysis (GPCA) to determine the load-up/load-shedding status of a motor and diagnose faults in its inverter. Most current methods for detecting OC faults are constrained by changes in the current amplitude and frequency, potentially leading to misjudgments during load-up/load-shedding transient states. The proposed method addresses this issue. Initially, this paper employs a homogenization method to process current data, eliminating the impact of transient processes during motor load-up/load-shedding states on inverter fault diagnosis. Subsequently, the fast Fourier transform (FFT) is used to extract the frequency domain characteristics of the data. If the PCA method is trained with a singular matrix, this can lead to an unreliable result. This paper introduces a generalization layer based on the PCA method, leading to the GPCA method, which enables training with singular matrices. The GPCA method is then developed to compute data features. By presetting thresholds and utilizing the prediction error value and contribution rate index of the GPCA method, the relevant state of the motor drive system can be determined. Finally, through simulations and experiments, it has been demonstrated that the method, using data from the stable working state, can effectively detect the working status of a motor and diagnose OC faults in its inverter, with a diagnostic time of 0.05 current cycles.

This paper proposes an improved dual-center particle swarm optimization (IDCPSO) algorithm which can effectively improve some inherent defects of particle swarm optimization algorithms such as being prone to premature convergence and low optimization accuracy. Based on the in-depth analysis of the velocity updating formula, the most innovative feature is the vectorial decomposition of the velocity update formula of each particle to obtain three different flight directions. After combining these three directions, six different flight paths and eight intermediate positions can be obtained. This method allows the particles to search for the optimal solution in a wider space, and the individual extreme values are greatly improved. In addition, in order to improve the global extreme value, it is designed to construct the population virtual center and the optimal individual virtual center by using the optimal position and the current position searched by the particle. Combining the above strategies, an adaptive mutation factor that accumulates the coefficient of mutation according to the number of iterations is added to make the particle escape from the local optimum. By running the 12 typical test functions independently 50 times, the results show an average improvement of 97.9% for the minimum value and 97.7% for the average value. The IDCPSO algorithm in this paper is better than other improved particle swarm optimization algorithms in finding the optimum.

Credit risk assessment is an important process in bank financial risk management. Traditional machine-learning methods cannot solve the problem of data islands and the high error rate of two-way decisions, which is not conducive to banks’ accurate credit risk assessment of users. To this end, this paper establishes a federated three-way decision incremental naive Bayes bank user credit risk assessment model (FTwNB) that supports asymmetric encryption, uses federated learning to break down data barriers between banks, and uses asymmetric encryption to protect data security for federated processes. At the same time, the model combines the three-way decision methods to realize the three-way classification of user credit (good, bad and delayed judgment), so as to avoid the loss of bank interests caused by the forced division of uncertain users. In addition, the model also incorporates incremental learning steps to eliminate training samples with poor data quality to further improve the model performance. This paper takes German Credit data and Default of Credit Card Clients data as examples to conduct simulation experiments. The result shows that the performance of the FTwNB model has been greatly improved, which verifies that it has good credit risk assessment capabilities.

Mission scheduling is an essential function of the management control of remote-sensing satellite application systems. With the continuous development of remote-sensing satellite applications, mission scheduling faces significant challenges. Existing work has many inherent shortcomings in dealing with dynamic task scheduling for remote-sensing satellites. In high-load and complex remote sensing task scenarios, there is low scheduling efficiency and a waste of resources. The paper proposes a scheduling method for remote-sensing satellite applications based on dynamic task prioritization. This paper combines the and Bound methodologies with an onboard task queue scheduling band in an active task prioritization context. A purpose-built emotional task priority-based scheduling blueprint is implemented to mitigate the flux and unpredictability characteristics inherent in the traditional satellite scheduling paradigm, improve scheduling efficiency, and fine-tune satellite resource allocation. Therefore, the Branch and Bound method in remote-sensing satellite task scheduling will significantly save space and improve efficiency. The experimental results show that comparing the technique to the three heuristic algorithms (GA, PSO, DE), the BnB method usually performs better in terms of the maximum value of the objective function, always finds a better solution, and reduces about 80% in terms of running time.