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We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

This issue of featured papers from 2020 is related to the study of symmetry phenomena in various different fields, but mainly in theoretical physics [...]

This editorial is a short review of papers accepted in the Mathematics and Symmetry/Asymmetry section in 2020–2021 about the symmetry methods [...]

This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...]

Role-based access control (RBAC) is a widely adopted access control model in various domains for defining security management. Role mining is closely related to role-based access control, as the latter employs role assignments to offer a flexible and scalable approach to managing permissions within an organization. The edge role mining problem (Edge RMP), a variant of the role mining problem (RMP), has long been recognized as an effective strategy for role assignment. Role mining, which groups users with similar access permissions into the same role, bears some resemblance to symmetry. Symmetry categorizes objects or graphics with identical characteristics into one group. Both involve a certain form of “classification” or “induction”. Edge-RMP reduces the associations between users and permissions, thereby lowering the security risks faced by the system. While an algorithm based on Boolean matrix factorization exists for this problem, it fails to further refine the resulting user–role assignment (UA) and role–permission assignment (PA) relationships. Additionally, this algorithm does not address constraint-related issues, such as cardinality constraints, user exclusion constraints, and user capabilities. Furthermore, it demonstrates significant redundancy of roles when handling large datasets, leaving room for further optimization of Edge-RMP results. To address these concerns, this paper proposes the MFC-RMA algorithm based on Boolean matrix factorization. The method achieves significant optimization of Edge-RMP results by handling relationships between roles possessing various permissions. Furthermore, this paper clusters, compresses, modifies, and optimizes the original data based on the similarity between users, ensuring its usability for role mining. Both theoretical and practical considerations are taken into account for different types of constraints, and algorithms are devised to reallocate roles incorporating these constraints, thereby generating UA and PA matrices. The proposed approach yields optimal numbers of generated roles and the sum of the minimum number of generated edges to address the aforementioned issues. Experimental results demonstrate that the algorithm reduces management overhead, provides efficient execution results, and ensures the accuracy of generated roles.

Abstract: This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model.

In this paper, a stability analysis and the controller improvement of T-S fuzzy Descriptor system are studied. Firstly, by making full use of the related theory of fuzzy affiliation function and combining the design method of fuzzy Lyapunov function with the method of inequality deflation, a stability condition with wider admissibility and less system conservatism is proposed. The advantage of this method is that it is not necessary to ensure that each fuzzy subsystem is progressively stable. We also maximise the boundary of the derivatives of the affiliation function mined. Secondly, a PDC controller and a Non-PDC controller are designed, and the deflation conditions for the linear matrix inequalities of the two controllers are constructed. Finally, some arithmetic simulations and practical examples are given to demonstrate the effectiveness of the method studied in this paper, and the results obtained are less conservative and have larger feasible domains than previous methods.

The effects of the helical trajectories of the perturbing electrons in magnetized plasmas on the dynamical Stark width of hydrogen or deuterium spectral lines have been studied analytically in our previous two papers—specifically in the situation where the magnetic field B is so strong that the dynamical Stark width of these lines reduces to the so-called adiabatic Stark width because the so-called nonadiabatic Stark width is completely suppressed. This situation corresponds, for example, to DA and DBA white dwarfs. We obtained those analytical results by using the formalism of the so-called conventional (or standard) theory of the impact Stark broadening: namely, by performing calculations in the second order of the Dyson perturbation expansion. The primary outcome was that the dynamical Stark broadening was found to not depend on the magnetic field B (for sufficiently strong B). In the present paper, we use the O4 symmetry of hydrogen atoms for performing the corresponding non-perturbative analytical calculations equivalent to accounting for all orders of the Dyson perturbation expansion. The results, obtained by using the O4 symmetry of hydrogen atoms, differ from our previous ones not only quantitatively, but—most importantly—qualitatively. Namely, the dynamical Stark broadening does depend on the magnetic field B, even for strong B. These results should be important for revising the interpretation of the hydrogen Balmer lines observed in DA and DBA white dwarfs. We also address confusion in the literature on this subject.

In active noise control (ANC) systems, the traditional filtered-x least mean square (FxLMS) algorithm has poor control effect on impulsive noise. To overcome this drawback, a robust cost function was designed in this paper by embedding the cost function of the FxLMS algorithm into the framework of hyperbolic tangent function; this paper thus proposes a robust filtered-x least hyperbolic tangent (FxLHT) algorithm in ANC systems. Moreover, the value of λ in the FxLHT algorithm greatly affects the robustness and convergence performance of the algorithm. Therefore, a variable λ-parameter was proposed to enhance the performance of the FxLHT algorithm. Simulation results show that in the active control of impulsive noise, compared with the FxLMS algorithm and other robust ANC algorithms, the proposed FxLHT algorithm and variable λ-parameter FxLHT algorithm not only exhibit good robustness and noise reduction performance but also have a better tracking ability.

This paper improves the timeliness of satellite mission planning to cope with the rapid response to changes. In this paper, satellite mission planning is investigated. Firstly, the satellite dynamics model and mission planning model are established, and an improved Monte Carlo tree (Improved-MCTS) algorithm is proposed, which utilizes the Monte Carlo tree search in combination with the state uncertainty network (State-UN) to reduce the time of exploring the nodes (At the MCTS selection stage, the exploration of nodes specifically refers to the algorithm needing to decide whether to choose nodes that have already been visited (exploitation) or nodes that have not been visited yet (exploration)). The results show that this algorithm performs better in terms of profit (in this paper, the observation task is given a weight of 0–1, and each planned task will receive a profit; that is, a profit will be assigned at the initial moment) and convergence speed compared to the ant colony algorithm (ACO) and the asynchronous advantage actor critic (A3C).

This paper presents an innovative mathematical model of solid fuel gasification, which is not described in the available literature. The calculation of the components of the heterogeneous phase (including both solid and gaseous phases) as well as the calculation of the homogeneous phase (only gaseous components) is based on the balance of the total amounts of carbon, oxygen, hydrogen, and nitrogen entering the reactor space. Additionally, this paper introduces a new method for calculating the composition of the gaseous phase, based on reducing the heterogeneous mixture (composed of solid and gaseous phases) to a homogeneous gaseous phase. This approach to calculating the gaseous phase composition in the solid fuel gasification process has not been found by the authors in the cited literature. This paper also presents a model for calculating the heterogeneous and gaseous phases using the number of moles that participate in the assumed chemical reactions of the solid fuel gasification process. This approach to calculating the composition of the heterogeneous and gaseous phases of the solid fuel gasification process is also not represented in the cited literature. For comparison with the literature data, municipal solid waste (MSW) and cashew nut shell (Cashew Shell Char (CNSC)) were used as fuels in the calculation of gasification composition. The results of the calculation of the gaseous phase composition using the model presented in the paper show good agreement with the data from the literature. The calculation of the composition of the heterogeneous mixture during the steam gasification of MSW (α = 0.4) shows the presence of a solid phase (carbon) up to approximately 735 °C. At that temperature, the synthetic gas contains only gaseous components: CO = 33.10%, H2 = 52.70%, CH4 = 2.54%, CO2 = 4.97, H2O = 5.93% and N2 = 0.76%. Increasing the temperature above 735 °C eliminates the solid phase from the equilibrium mixture. The literature data on solid fuel gasification generally do not consider the proportion of the solid phase (carbon) in the equilibrium mixture. To satisfy the material balance at the input and output of the gasification reactor, it is necessary to determine the proportion of the solid phase (carbon) in the equilibrium mixture. Since the proportion of the solid phase (carbon) in the heterogeneous equilibrium mixture can only be determined through measurement, the development and application of a mathematical model in engineering practice is of great importance, so this developed model can be considered a useful tool for simulating the influence of process parameters on gas characteristics.

Convolutional neural networks (CNNs) have achieved remarkable success in fully supervised medical image segmentation tasks. However, the acquisition of large quantities of homogeneous labeled data is challenging, making semi-supervised training methods that rely on a small amount of labeled data and pseudo-labels increasingly popular in recent years. Most existing semi-supervised learning methods, however, underestimate the importance of the unlabeled regions during training. This paper posits that these regions may contain crucial information for minimizing the model’s uncertainty prediction. To enhance the segmentation performance of the left-atrium database, this paper proposes a triple consistency segmentation network based on the squeeze-and-excitation mechanism (SETC-Net). Specifically, the paper constructs a symmetric architectural unit called SEConv, which adaptively recalibrates the feature responses in the channel direction by modeling the inter-channel correlations. This allows the network to adaptively weigh each channel according to the task’s needs, thereby emphasizing or suppressing different feature channels. Moreover, SETC-Net is composed of an encoder and three slightly different decoders, which convert the prediction discrepancies among the three decoders into unsupervised loss through a constructed iterative pseudo-labeling scheme, thus encouraging consistent and low-entropy predictions. This allows the model to gradually capture generalized features from these challenging unmarked regions. We evaluated the proposed SETC-Net on the public left-atrium (LA) database. The proposed method achieved an excellent Dice score of 91.14% using only 20% of the labeled data. The experiments demonstrate that the proposed SETC-Net outperforms seven current semi-supervised methods in left-atrium segmentation and is one of the best semi-supervised segmentation methods on the LA database.

In this paper, we propose a precise Wigner–Weyl calculus for the models defined on the honeycomb lattice. We construct two symbols of operators: the B symbol, which is similar to the one introduced by F. Buot, and the W (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner-transformed Green function. This expression may be used for the description of the systems with artificial honeycomb lattice, when magnetic flux through the lattice cell is of the order of elementary quantum of magnetic flux. It is worth mentioning that, in the present paper, we do not consider the effect of interactions.

In this paper, we focus on a fractional differential equation 0CDαu(t)+q(t)u(t)=0 with boundary value conditions u(0)=δu(1),u′(0)=γu′(1). The paper begins by pointing out the inadequacies of the study conducted by Ma and Yangin establishing Lyapunov-type inequalities. It then discusses the properties of its Green’s function and investigates extremum problems related to several linear functions. Finally, thorough classification and analysis of various cases for parameters δ and γ are conducted. As a result, a comprehensive solution corresponding to the Lyapunov-type inequality is obtained.

The accurate evaluation of green innovation efficiency is a critical prerequisite for enterprises to achieve sustainable development goals and improve environmental performance and economic efficiency. This paper evaluates the green innovation efficiency of 72 new-energy enterprises by using a hybrid method of Data Envelopment Analysis (DEA) and a random forest model. The non-parametric DEA model is combined with the parametric SFA model to analyze the real green innovation efficiency on the basis of removing environmental factors and random factors. Then, the random forest model based on a nonlinear relationship is used to evaluate factors impacting green innovation efficiency. This paper proposes a comprehensive evaluation method designed to assess the green innovation efficiency of new-energy enterprises. By applying this method, companies can gain a comprehensive understanding of the current performance in green innovation, facilitating informed decision-making and accelerating sustainable development.

In this paper, several classes of rough Marcinkiewicz integral operators along surfaces of revolution on product spaces are investigated. We prove the Lp boundedness of these operators when their kernels functions belong to a class of functions related to a class of functions introduced by Grafakos-Stefanov. The results in this paper extend and improve several known results on Marcinkiewicz integrals over a symmetric space.

The primary objective of this paper is to address the challenge of designing finite-time fault-tolerant control mechanisms for nonlinear flexible spacecraft systems, which are particularly vulnerable to randomized actuator faults. Diverging from traditional methodologies, our research harnesses the capabilities of the Takagi–Sugeno (T–S) fuzzy framework. A unique feature of our model is the representation of actuator failures as stochastic signals following a Markov process, thereby offering a robust solution for addressing timeliness concerns. In this paper, we introduce a generalized reciprocally convex inequality that includes adjustable parameters, broadening the scope of previous results by accommodating them as special cases. Through the amalgamation of this enhanced inequality and flexible independent parameters, we propose an innovative controller design strategy. This approach establishes a stability standard that guarantees mean-square H∞ performance. In order to validate the efficacy of the suggested strategy, we present a numerical illustration involving a nonlinear spacecraft system, showcasing the practical advantages and feasibility of our proposed technique.

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields.

The frequency support capacity of power loads is essential for maintaining active power symmetry and balance between the generation and demand sides of power systems. As the proportion of renewable energy sources and power electronic equipment increases, the inertia on the power generation side decreases, highlighting the growing importance of frequency support on the load side. As it is generally believed that the active power balance of power systems determines the frequency stability, few studies have considered the effect of voltage variation on the frequency response dynamics. It is important to note that the node voltage keeps fluctuating throughout the frequency dynamic process, which affects the active power of loads and should not be neglected. Based on the aforementioned rationales, this paper endeavors to investigate the modeling of power load frequency response and analyze its support capability considering the voltage variation effect. This paper initially establishes the small-signal model of dynamic load under frequency dynamics, derives the transfer function relating active power to system frequency deviation, and subsequently develops its frequency response model. Subsequently, commencing with the ZIP model of static load, the power fluctuation of load nodes is derived from the influence of preceding nodes, and the frequency response model of the static load is formulated and its frequency support capacity is scrutinized. Based on this foundation, a comprehensive aggregation model of the complex load is constructed, and its frequency support capability is assessed using actual data. Finally, the proposed model and analysis results are validated through simulation, confirming their correctness and effectiveness.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The obtained result is the approximation of the real value. Currently, there are few reports on the approximate error and applicable condition. In this paper, we study the factors related to the approximate errors according to the fractional expansions. Our research shows that the approximate errors relate not only to fractional order but also to time t, and that they increase rapidly with time t. This method can only be applied within a certain time range, and the time range is relevant to fractional order and fractional expansions. We can ascertain this time range according to the absolute error and the relative error. Many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem.

This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality.

Forest resources are renewable, and the rational exploitation and utilization of forest resources are not only conducive to sustainable development on a population scale, they can also lead to higher economic benefits. Based on the actual timber harvest problem, this paper establishes the joint harvest model of timber and non-timber with nonlinear harvest items. In the numerical simulation, by comparing the existing proportional harvest model, it is concluded that the optimal harvest strategy of nonlinear harvest items in this paper can obtain larger ecological benefits and be more conducive to the sustainable development of a population. Firstly, using the qualitative theory of ordinary differential equations, the dynamic behavior of the model is studied, and the existence and stability of the equilibrium point of the model are proven. Secondly, the optimal control solution is obtained by using the optimal control theory. Finally, the optimal harvesting strategy of timber and non-timber products is given based on the numerical simulation results, and a comparison of the effects of different parameters on the optimal harvest strategy, which provides a certain theoretical basis for the sustainable development of the ecological economy of forestry, is carried out.

The efficiency of mechanical crushing is a key metric for evaluating machinery performance. However, traditional contact-based methods for measuring this efficiency are unable to provide real-time data monitoring and can potentially disrupt the production process. In this paper, we introduce a non-contact measurement technique for mechanical crushing efficiency based on deep learning algorithms. This technique utilizes close-range imaging equipment to capture images of crushed particles and employs deeply trained algorithmic programs rooted in symmetrical logical structures to extract statistical data on particle size. Additionally, we establish a relationship between particle size and crushing energy through experimental analysis, enabling the calculation of crushing efficiency data. Taking cement crushing equipment as an example, we apply this non-contact measurement technique to inspect cement particles of different sizes. Using deep learning algorithms, we automatically categorize and summarize the particle size ranges of cement particles. The results demonstrate that the crushing efficiencies of ore crushing particles, raw material crushing particles, and cement crushing particles can respectively reach 80.7%, 70.15%, and 80.27%, which exhibit a high degree of consistency with the rated value of the samples. The method proposed in this paper holds significant importance for energy efficiency monitoring in industries that require mechanical crushing.

The operational stability of a power transformer exerts an extremely important impact on the power symmetry, balance, and security of power systems. When the grid load fluctuates greatly, if the load factor of the transformer cannot be maintained within a reasonable range, it leads to increased instability in grid operation. Adjusting the transformer capacity based on load changes is of great significance. The existing control methods for on-load capacity-regulating (OLCR) transformers have low timeliness, and the daily switching frequency of the capacity-regulating switch is not controlled. To ensure the safe and stable operation of transformers, this paper proposes a control method for OLCR transformers based on load prediction and fuzzy control. Firstly, the operating principle of OLCR transformers is analyzed, and a multi-strategy enhanced dung beetle optimizer (MSDBO) combined with a CNN−LSTM model is proposed for load forecasting. On this basis, the daily switching frequency of the capacity-regulating transformer is introduced, and hesitant fuzzy control is used to select the optimal capacity-regulating strategy relying on three factors: loss, economy, and switching frequency. Finally, simulation models are constructed using the MATLAB/SIMULINK platform and simulation analysis is conducted to verify the effectiveness and superiority of the proposed control method. For the three scenarios in this paper, the method reduces daily power loss by 28.5% to 56.3% and daily operating costs by 25.4% to 50.8%. The method used in this paper can sacrifice 3.5% to 9.2% of the loss reduction capability in exchange for reducing the number of switch operations by 28.6% to 57.1%, significantly extending the lifespan of the switches and thereby increasing the operational lifespan of the transformer.

In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system.

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators.

Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer’s supply, and distributor’s demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model.

The modular robotic arms can achieve desired performances in different scenarios through the combination of various modules, and concurrently hold the potential to exhibit geometric symmetry and uniform mass symmetry. Therefore, selecting the appropriate combination of modules is crucial for realizing the functions of the robotic arm and ensuring the elegance of the system. To this end, this paper proposes a double deep Q-network (DDQN)-based configuration design algorithm for modular robotic arms, which aims to find the optimal configuration under different tasks. First, a library of small modules of collaborative robotic arms consisting of multiple tandem robotic arms is constructed. These modules are described in a standard format that can be directly imported into the software for simulation, providing greater convenience and flexibility in the development of modular robotic arms. Subsequently, the DDQN design framework for module selection is established to obtain the optimal robotic arm configuration. The proposed method could deal with the overestimation problem in the traditional deep Q-network (DQN) method and improve the estimation accuracy of the value function for each module. In addition, the experience replay mechanism is improved based on the SumTree technique, which enables the algorithm to make effective use of historical experience and prevents the algorithm from falling into local optimal solutions. Finally, comparative experiments are carried out on the PyBullet simulation platform to verify the effectiveness and superiority of the configuration design method developed in the paper. The simulation results show that the proposed DDQN-based method with experience replay mechanism has higher search efficiency and accuracy compared to the traditional DQN scheme.

This paper considers a nonlinear fractional-order boundary value problem HDa,gα1,β,μx(t)+f(t,x(t),HDa,gα2,β,μx(t))=0, for t∈[a,b], α1∈(1,2], α2∈(0,1], β∈[0,1] with appropriate integral boundary conditions on the Hölder spaces. Here, f is a real-valued function that satisfies the Hölder condition, and HDa,gα,β,μ represents the tempered-Hilfer fractional derivative of order α>0 with parameter μ∈R+ and type β∈[0,1]. The corresponding integral problem is introduced in the study of this issue. This paper addresses a fundamental issue in the field, namely the circumstances under which differential and integral problems are equivalent. This approach enables the study of differential problems using integral operators. In order to achieve this, tempered fractional calculus and the equivalence problem of the studied problems are introduced and studied. The selection of an appropriate function space is of fundamental importance. This paper investigates the applicability of these operators on Hölder spaces and provides a comprehensive rationale for this choice.

To ensure precise positioning of the macro–micro platform with a symmetrical structure, it is crucial to mitigate the impact of various perturbations, including disturbances, as well as complex factors such as external loads, electrical noise, and model parameter variations. This paper proposes a novel macro–micro master–slave control structure that incorporates adaptive fuzzy linear active disturbance rejection control (AFLADRC). The Kp and Kd parameters of the linear state error feedback (LSEF) are dynamically tuned and adjusted using fuzzy reasoning. This approach enhances the robustness of the system and simplifies the tuning process. In addition, this paper also analyzes the symmetry of the coupling effect between macro and micro, as the coupling will affect the motor force and the reaction potential of the motor. The macro–micro platform adopts a symmetric design; the macro stage is driven by a permanent magnet synchronous linear motor (PMLSM), and the micro stage is driven by a voice coil motor. Finally, we built the macro–micro linear motion experimental platform to verify the control effect of the proposed method by conducting trajectory tracking experiments and comparison experiments.

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph.

Target detection algorithms can greatly improve the efficiency of tomato leaf disease detection and play an important technical role in intelligent tomato cultivation. However, there are some challenges in the detection process, such as the diversity of complex backgrounds and the loss of leaf symmetry due to leaf shadowing, and existing disease detection methods have some disadvantages in terms of deteriorating generalization ability and insufficient accuracy. Aiming at the above issues, a target detection model for tomato leaf disease based on deep learning with a global attention mechanism, TDGA, is proposed in this paper. The main idea of TDGA includes three aspects. Firstly, TDGA adds a global attention mechanism (GAM) after up-sampling and down-sampling, as well as in the SPPF module, to improve the feature extraction ability of the target object, effectively reducing the interference of invalid targets. Secondly, TDGA uses a switchable atrous convolution (SAConv) in the C3 module to improve the model’s ability to detect. Thirdly, TDGA adopts the efficient IoU loss (EIoU) instead of complete IoU loss (CIoU) to solve the ambiguous definition of aspect ratio and sample imbalance. In addition, the influences of different environmental factors such as single leaf, multiple leaves, and shadows on the performance of tomato disease detection are extensively experimented with and analyzed in this paper, which also verified the robustness of TDGA. The experimental results show that the average accuracy of TDGA reaches 91.40%, which is 2.93% higher than that of the original YOLOv5 network, which is higher than YOLOv5, YOLOv7, YOLOHC, YOLOv8, SSD, Faster R-CNN, RetinaNet and other target detection networks, so that TDGA can be utilized for the detection of tomato leaf disease more efficiently and accurately, even in complex environments.

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from φ-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of α-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself.

Community detection can help analyze the structural features and functions of complex networks, and plays important roles in many aspects such as project recommendation and network evolution analysis. Therefore, community detection has always been a hot topic in the field of complex networks. Although various community-detection methods have been proposed, how to improve their accuracy and efficiency is still an ambition pursued by researchers. In view of this, this paper proposes a community-detection method for complex networks based on node influence analysis. First, the influence of nodes is represented as a vector composed by neighborhood degree centrality, betweennes centrality and clustering coefficient. Then, Pareto dominance is used to rank the influence of nodes. After that, the community centers are selected by comprehensively considering the node influence and crowding degree. Finally, the remaining nodes are allocated to different communities using a labeling algorithm. The proposed method in this paper is applied to several actual networks. The comparison results with other methods demonstrate the effectiveness of the proposed method.

With the ongoing advancements in material technology, the domain of soft robotics has garnered increasing attention. Soft robots, in contrast to their rigid counterparts, offer superior adaptability to the environment, enhanced flexibility, and improved safety, rendering them highly suitable for complex application scenarios such as rescue operations and medical interventions. In this paper, a new type of pneumatic software actuator is proposed. The actuator adopts a combination of a soft structure and pneumatic control, which is highly flexible and versatile. By using the flow of gas inside the soft structure, high-precision and flexible motion control is realized. In the design process, the extensibility and adaptability of the structure are considered, so that the actuator can adapt to different working environments and task requirements. The experimental results show that the pneumatic soft actuator exhibits excellent performance in terms of accuracy, response speed, and controllability. This research provides new ideas and methods for the development of the field of pneumatic actuators and has wide application prospects. The main research content of this paper is as follows: first, the soft pneumatic actuator is modeled and simulated, the structure is optimized on the basis of simulation, and finally, the performance of the actuator is tested.

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two types of full moment problems are provided. The only given data are the moments of all positive integer orders of the solution and two other linear, not necessarily positive, constraints on it. Under natural assumptions, all the linear solutions are continuous. With their value in the subspace of polynomials being given by the moment conditions, the uniqueness follows. When the involved linear solutions and constraints are positive, the sufficient conditions mentioned above are also necessary. This is achieved in the third part of the paper. All these conditions are written in terms of quadratic expressions.

This paper presents the numerical solution of the heat conduction model with a fractional derivative of the Riemann–Liouville type with respect to the spatial variable. The considered mathematical model assumes the dependence on temperature of the material parameters (such as specific heat, density, and thermal conductivity) of the model. In the paper, the boundary conditions of the first and second types are considered. If the heat flux equal to zero is assumed on the left boundary, then the thermal symmetry is obtained, which results in a simplification of the problem and the possibility of considering only half the area. The numerical examples presented in the paper illustrate the effectiveness and convergence of the discussed computational method.

The pointing accuracy of large radio telescopes is affected by antenna structure errors, installation errors, servo errors, gravity, and varying environmental factors. Although an on-line pointing model had been developed in the past for several large radio telescopes to correct these effects, it is also valuable to explore new ways to correct these effects. Therefore, in order to estimate the dynamic pointing error of large radio telescopes under solar radiation, a new way based on digital twin (DT) is used in this paper. Digital models of the Wuqing 70-m radio telescope (WRT70) are created based on the DT operational framework. Finally, the reliability of the WRT70’s DT system is verified, and the dynamic pointing error of WRT70 (staying at the position of the elevation angle of 90° and the azimuth angle of 180°) on two sunny days in different seasons is estimated by the created DT system. The research results show that the pointing error of large radio telescopes under solar radiation fluctuates greatly and the seasonal differences are very striking. The maximum elevation pointing error of WRT70 under solar radiation around the winter solstice is over 40 arcsec, which is equal to 4/11 of the beam width for WRT70 operating at 8 GHz. In this paper, it is feasible to estimate the time-varying pointing errors of large radio telescopes at rest under solar radiation by constructing a DT system, but it is not effective to estimate the dynamic pointing errors of large radio telescopes in operation. It is expected to establish a dynamic pointing error model and calibrate the dynamic pointing errors of large radio telescopes in operation by DT technology in the future.

The algorithms for determining the active space object maneuver parameters in the conditions of near-circular orbits are presented in the paper. The right ascension and declination angles are used to determine the parameters of a single maneuver with transversal and lateral components (the application moment and the velocity impulse magnitude). Two pairs of angles are used to determine the parameters of the maneuver with only a lateral component. Two pairs of angles are needed for the determination of the parameters of the long-duration maneuver performed by a low-thrust engine (moments of the maneuver start and finish, and components of the acceleration delivered by the engine). The essential detail that makes it possible to determine the parameters of long-duration maneuvers is their symmetry relative to the center of the engine operating interval. Considerable perturbing accelerations, which are not accounted for by traditional perturbing models, affect passive objects, especially membranous objects with a big and variable area-to-mass ratio. This decreases dramatically the accuracy of these objects’ motion propagation. In this paper, the magnitude of perturbing acceleration is determined with the assumption that it is constant and is active throughout the whole time interval from the moment of the last orbit determination to the moment of the new measurement used. Examples of the assessment of maneuvers performed by an object in the geostationary orbit are presented.

Cavitation bubbles near narrow gaps widely exist within microfluidic control devices. In the present paper, a laser-induced cavitation bubble is arranged in a narrow gap composed of two parallel plates. The inception position of the bubble is set to be at the same distance from the two plates so that the dynamic behaviors of the bubble are symmetrical. The collapse and rebound dynamics of the bubble near the boundary of a narrow gap are investigated through high-speed photography. The bubble behaviors (e.g., shape deformation, translational movement, and jet characteristics) are analyzed while considering the influence of the dimensionless distance between the bubble and the boundary and the dimensionless gap width. The principal findings include the following: (1) When the dimensionless distance is small, a violent jet towards the gap is generated during the bubble collapse stage, along with a weak counter-jet towards the boundary appearing during the rebound stage. (2) As the dimensionless distance increases, the translational distance of the bubble during the collapse stage initially decreases, then increases, and finally decreases to zero. (3) Within the parameter range considered in this paper, the dimensionless width mainly affects the expansion degree and movement direction of the bubble cloud during its rebound and subsequent stages. The above research findings can provide experimental support for bubble-driven flow control, pumping, and liquid mixing in microfluidic channels.

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism.

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.

With the continuous development and progress of wireless self-organizing network communication technology, how to carry out long-distance cooperative control of multiple intelligences under the framework of an air–ground integrated wireless high-mobility self-organizing network has become a hot and difficult topic that needs to be solved urgently. This paper takes the air–ground integrated wireless high-mobility self-organizing network system as the basic framework and focuses on solving the long-distance cooperative fault-tolerant control of multi-intelligent bodies and the topological stability of a wireless mobile self-organizing network. To solve the above problems, a direct neural network with a robust adaptive fault-tolerant controller is designed in this paper. By constructing a symmetric population neural network model and combining it with the Lyapunov stabilization criterion, the system feedback matrix K has the ability of autonomous adaptive learning, and symmetrically distorts, rotates, or scales the training data to instantly adjust the system’s fault-tolerant corrections and adaptive adjusting factors to resist the unknown disturbances and faults, to achieve the goals of multi-intelligent body stable control and the stable operation of a wireless high-mobility self-organizing network topology. Simulation results show that with the feedback adjustment of the multi-system under the designed controller, the multi-system as a whole has good fault-tolerant performance and autonomous learning approximation performance, and the tracking error asymptotically converges to zero. The experimental results show that the multi-flight subsystems fly stably, the air–ground integrated wireless high-mobility self-organizing network topology has good stability performance, and the maximum relative improvement of the topology stability performance is 50%.

One of the limitations of the dung beetle optimization (DBO) is its susceptibility to local optima and its relatively low search accuracy. Several strategies have been utilized to improve the diversity, search precision, and outcomes of the DBO. However, the equilibrium between exploration and exploitation has not been achieved optimally. This paper presents a novel algorithm called the ODBO, which incorporates cat map and an opposition-based learning strategy, which is based on symmetry theory. In addition, in order to enhance the performance of the dung ball rolling phase, this paper combines the global search strategy of the osprey optimization algorithm with the position update strategy of the DBO. Additionally, we enhance the population’s diversity during the foraging phase of the DBO by incorporating vertical and horizontal crossover of individuals. This introduction of asymmetry in the crossover operation increases the exploration capability of the algorithm, allowing it to effectively escape local optima and facilitate global search.

Network traffic classification is crucial for identifying network applications and defending against network threats. Traditional traffic classification approaches struggle to extract structural features and suffer from poor interpretability of feature representations. The high symmetry between network traffic classification and its interpretable feature representation is vital for network traffic analysis. To address these issues, this paper proposes a traffic classification and feature representation model named the attention mechanism autoencoder (AMAE). The AMAE model extracts the global spatial structural features of network traffic through attention mechanisms and employs an autoencoder to extract local structural features and perform dimensionality reduction. This process maps different network traffic features into one-dimensional coordinate systems in the form of spectra, termed FlowSpectrum. The spectra of different network traffic represent different intervals in the coordinate system. This paper tests the interpretability and classification performance of network traffic features of the AMAE model using the ISCX-VPN2016 dataset. Experimental results demonstrate that by analyzing the overall distribution of attention weights and local weight values of network traffic, the model effectively explains the differences in the spectral representation intervals of different types of network traffic. Furthermore, our approach achieves the highest classification accuracy of up to 100% for non-VPN-encrypted traffic and 99.69% for VPN-encrypted traffic, surpassing existing traffic classification schemes.

This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation.

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine’s notions of generalized closed sets and Maki’s Λ sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine’s generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine’s method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of Λ-sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial.