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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 [...]

The International Institute of Knowledge Innovation and Invention (IIKII) is an institute that promotes the exchange of innovations and inventions, and establishes a communication platform for international innovations and researches. In 2019, IIKII cooperated with the Institute of Electrical and Electronics Engineers (IEEE) Tainan Section Sensors Council to hold IEEE conferences such as IEEE ICIASE 2019, IEEE ECBIOS 2019, IEEE ICKII 2019, ICUSA-GAME 2019, and IEEE ECICE 2019. This Special Issue entitled “Selected Papers from IIKII 2019 conferences” aims to select excellent papers from IIKII 2019 conferences, including symmetry in physics, chemistry, biology, mathematics, and computer science, etc. It selected 21 excellent papers from 750 papers presented in IIKII 2019 conferences on the topic of symmetry. The main goals of this Special Issue are to encourage scientists to publish their experimental and theoretical results in as much detail as possible, and to discover new scientific knowledge relevant to the topic of symmetry.

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

Over the past four decades, the prophecy from computer pundits and prognosticators pointed to the looming arrival of the paperless office era. However, forty years later, physical paper documents are still playing a significant role due to the ease of use, superior readability, and availability. The drawbacks of paper sheets are that they are hard to modify and retrieve, have limited space, and are environmentally unfriendly. Augmenting paper documents with digital information from mobile devices extends the two-dimensional space of physical paper documents. Various camera-based recognition and detection devices have been proposed to augment paper documents with digital information. However, there are still some limitations that exist in these systems. This paper presents a novel, low cost, spatially aware, mobile system called Ultrasonic PhoneLens. The Ultrasonic PhoneLens adopts two-dimensional dynamic image presentation and ultrasonic sound positioning techniques. It consists of two ultrasonic sound sensors, one Arduino mini-controller board, and one android mobile device. Based on the location of the mobile device over the physical paper, Ultrasonic PhoneLens can retrieve pre-saved digital information from a mobile database for the object (such as a text, a paragraph, or an image) in a paper document. An empirical study was conducted to evaluate the system performance. The results indicate that our system has a better performance in tasks such as browsing multivalent documents and sharing digital information than the Wiimote PhoneLens system.

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids.

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić’s method, which generalizes Banach’s theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić’s approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić’s works while providing valuable insights into this specialized domain.

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies’ green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality.

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient.

Since plant diseases occurring during the growth process are a significant factor leading to the decline in both yield and quality, the classification and detection of plant leaf diseases, followed by timely prevention and control measures, are crucial for safeguarding plant productivity and quality. As the traditional convolutional neural network structure cannot effectively recognize similar plant leaf diseases, in order to more accurately identify the diseases on plant leaves, this paper proposes an effective plant disease image recognition method aECA-ResNet34. This method is based on ResNet34, and in the first and the last layers of this network, respectively, we add this paper’s improved aECAnet with the symmetric structure. aECA-ResNet34 is compared with different plant disease classification models on the peanut dataset constructed in this paper and the open-source PlantVillage dataset. The experimental results show that the aECA-ResNet34 model proposed in this paper has higher accuracy, better performance, and better robustness. The results show that the aECA-ResNet34 model proposed in this paper is able to recognize diseases of multiple plant leaves very accurately.

The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples.

Occlusion or posture change of the face in natural scenes has typical asymmetry; however, an asymmetric face plays a key part in the lack of information available for facial expression recognition. To solve the problem of low accuracy of asymmetric facial expression recognition, this paper proposes a fusion of channel global features and a spatial local information expression recognition network called the “Channel–Spatial Integration Network” (CSINet). First, to extract the underlying detail information and deepen the network, the attention residual module with a redundant information filtering function is designed, and the backbone feature-extraction network is constituted by module stacking. Second, considering the loss of information in the local key area of face occlusion, the channel–spatial fusion structure is constructed, and the channel features and spatial features are combined to enhance the accuracy of occluded facial recognition. Finally, before the full connection layer, more local spatial information is embedded into the global channel information to capture the relationship between different channel–spatial targets, which improves the accuracy of feature expression. Experimental results on the natural scene facial expression data sets RAF-DB and FERPlus show that the recognition accuracies of the modeling approach proposed in this paper are 89.67% and 90.83%, which are 13.24% and 11.52% higher than that of the baseline network ResNet50, respectively. Compared with the latest facial expression recognition methods such as CVT, PACVT, etc., the method in this paper obtains better evaluation results of masked facial expression recognition, which provides certain theoretical and technical references for daily facial emotion analysis and human–computer interaction applications.

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX = C and XB = C. Finally, we provide a numerical example to demonstrate the findings of this paper.

In recent years, with the rapid development of deep learning technology, a large number of excellent convolutional neural networks (CNNs) have been proposed, many of which are based on improvements to classical methods. Based on the Inception family of methods, depthwise separable convolution was applied to Xception to achieve lightweighting, and Inception-ResNet introduces residual connections to accelerate model convergence. However, existing improvements for the Inception module often neglect further enhancement of its receptive field, while increasing the receptive field of CNNs has been widely studied and proven to be effective in improving classification performance. Motivated by this fact, three effective expansion modules are proposed in this paper. The first expansion module, Inception expand (Inception-e) module, is proposed to improve the classification accuracy by concatenating more and deeper convolutional branches. To reduce the number of parameters for Inception e, this paper proposes a second expansion module—Equivalent Inception-e (Eception) module, which is equivalent to Inception-e in terms of feature extraction capability, but which suppresses the growth of the parameter quantity brought by the expansion by effectively reducing the redundant convolutional layers; on the basis of Eception, this paper proposes a third expansion module—Lightweight Eception (Lception) module, which crosses depthwise convolution with ordinary convolution to further effectively reduce the number of parameters. The three proposed modules have been validated on the Cifar10 dataset. The experimental results show that all these extensions are effective in improving the classification accuracy of the models, and the most significant effect is the Lception module, where Lception (rank = 4) on the Cifar10 dataset improves the accuracy by 1.5% compared to the baseline model (Inception module A) by using only 0.15 M more parameters.

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data.

With the development of autonomous driving, consensus is gradually forming around vehicle–infrastructure cooperative (VIC) autonomous driving. The VIC environment-sensing system uses roadside sensors in collaboration with automotive sensors to capture traffic target information symmetrically from both the roadside and the vehicle, thus extending the perception capabilities of autonomous driving vehicles. However, the current target detection accuracy for feature fusion based on roadside LiDAR and automotive LiDAR is relatively low, making it difficult to satisfy the sensing requirements of autonomous vehicles. This paper proposes PAFNet, a VIC pillar attention fusion network for target detection, aimed at improving LiDAR target detection accuracy under feature fusion. The proposed spatial and temporal cooperative fusion preprocessing method ensures the accuracy of the fused features through frame matching and coordinate transformation of the point cloud. In addition, this paper introduces the first anchor-free method for 3D target detection for VIC feature fusion, using a centroid-based approach for target detection. In the feature fusion stage, we propose the grid attention feature fusion method. This method uses the spatial feature attention mechanism to fuse the roadside and vehicle-side features. The experiment on the DAIR-V2X-C dataset shows that PAFNet achieved a 6.92% higher detection accuracy in 3D target detection than FFNet in urban scenes.

For wireless sensor network (WSN) coverage problems, since the sensing range of sensor nodes is a circular area with symmetry, taking symmetry into account when deploying nodes will help simplify problem solving. In addition, in view of two specific problems of high node deployment costs and insufficient effective coverage in WSNs, this paper proposes a WSN coverage optimization method based on the improved grey wolf optimizer with multi-strategies (IGWO-MS). As far as IGWO-MS is concerned, first of all, it uses Sobol sequences to initialize the population so that the initial values of the population are evenly distributed in the search space, ensuring high ergodicity and diversity. Secondly, it introduces a search space strategy to increase the search range of the population, avoid premature convergence, and improve search accuracy. And then, it combines reverse learning and mirror mapping to expand the population richness. Finally, it adds Levy flight to increase the disturbance and improve the probability of the algorithm jumping out of the local optimum. To verify the performance of IGWO-MS in WSN coverage optimization, this paper rasterizes the coverage area of the WSN into multiple grids of the same size and symmetry with each other, thereby transforming the node coverage problem into a single-objective optimization problem. In the simulation experiment, not only was IGWO-MS selected, but four other algorithms were also selected for comparison, namely particle swarm optimization (PSO), grey wolf optimizer (GWO), grey wolf optimization based on drunk walk (DGWO), and grey wolf optimization led by two-headed wolves (GWO-THW). The experimental results demonstrate that when the number of nodes for WSN coverage optimization is 20 and 30, the optimal coverage rate and average coverage rate using IGWO-MS are both improved compared to the other four comparison algorithms. To make this clear, in the case of 20 nodes, the optimal coverage rate of IGWO-MS is increased by 13.19%, 1.68%, 4.92%, and 3.62%, respectively, compared with PSO, GWO, DGWO, and GWO-THW; while IGWO-MS performs even better in terms of average coverage rate, which is 16.45%, 3.13%, 11.25%, and 6.19% higher than that of PSO, GWO, DGWO, and GWO-THW, respectively. Similarly, in the case of 30 nodes, compared with PSO, GWO, DGWO, and GWO-THW, the optimal coverage rate of the IGWO-MS is increased by 15.23%, 1.36%, 5.55%, and 3.66%; the average coverage rate is increased by 16.78%, 1.56%, 10.91%, and 8.55%. Therefore, it can be concluded that IGWO-MS has certain advantages in solving WSN coverage problems, which is reflected in that not only can it effectively improve the coverage quality of network nodes, but it also has good stability.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

In this paper, we explore a model of an N-player, non-cooperative stochastic game, drawing inspiration from the discrete formulation of the red-and-black gambling problem, as initially introduced by Dubins and Savage in 1965. We extend upon the work of Pontiggia from 2007, presenting a main theorem that broadens the conditions under which bold strategies by all players can achieve a Nash equilibrium. This is obtained through the introduction of a novel functional inequality, which serves as a key analytical tool in our study. This inequality enables us to circumvent the restrictive conditions of super-multiplicativity and super-additivity prevalent in the works of Pontiggia and others. We conclude this paper with a series of illustrative examples that demonstrate the efficacy of our approach, notably highlighting its ability to accommodate a broader spectrum of probability functions than previously recognized in the existing literature.

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green’s function kernel. In the deterministic case, Green’s function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type.

This paper investigates various aspects of the distribution of roots and critical points of a complex polynomial, including their variance and the relationships between their moduli using an inequality due to de Bruijn. Making use of two other inequalities-again due to de Bruijn-we derive two probabilistic results concerning upper bounds for the average moduli of the imaginary parts of zeros and those of critical points, assuming uniform distribution of the zeros over a unit disc and employing the Markov inequality. The paper also provides an explicit formula for the variance of the roots of a complex polynomial for the case when all the zeros are real. In addition, for polynomials with uniform distribution of roots over the unit disc, the expected variance of the zeros is computed. Furthermore, a bound on the variance of the critical points in terms of the variance of the zeros of a general polynomial is derived, whereby it is established that the variance of the critical points of a polynomial cannot exceed the variance of its roots. Finally, we conjecture a relation between the real parts of the zeros and the critical points of a polynomial.

The aero-engine serves as the “heart” of an aircraft and is a primary factor determining the aircraft’s performance. Among the crucial components in the core of aero-engines, aero-engine compressor blades stand out as extremely important. They are not only numerous but also characterized by a multitude of parameters, making them the most complex parts in an aero-engine. This paper aims to address the trade-off between accuracy and efficiency in the existing measurement methods for asymmetric blades. Non-contact measurements were conducted using a structured light system composed of a stereo camera and a DLC projector. The point cloud data of the blades are processed using methods such as the PCA (Principal Component Analysis) algorithm, binary search, and least squares fitting. This paper established a fringe-projection profilometry light sensor system for the multi-view measurement of the blades. High-precision rotary tables are utilized to rotate and extract complete spatial point cloud data of aviation blades. Finally, measurements and comparative experiments on the blade body are conducted. The obtained blade point cloud data undergo sorting and denoising processes, resulting in improved measurement accuracy. The measurement error of the blade chord length is 0.001%, the measurement error of blade maximum thickness is 0.895%, compared to CMM (Coordinate Measuring Machine), where the measurement error of chord is 0.06%.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.

This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper.

The objective of portfolio diversification is to reduce risk and potentially enhance returns by spreading investments across different asset classes. Existing portfolio diversification models have traditionally been trained on historical financial time series data. However, several issues arise with historical financial time series data, making it challenging to train models effectively to achieve the portfolio diversification objective: an insufficient amount of training data and the uncertainty deficiency problem, wherein the uncertainty that existed in the past is not visible in the present. Insufficient datasets, characterized by small data size, result in information asymmetry and compromise portfolio performance. This limitation underscores the importance of adopting a pattern-centric data augmentation approach, capable of unveiling hidden patterns and structures within the financial time series data. To address these challenges, this paper introduces the financial time series decomposition-based variational encoder-decoder (FED) method to augment financial time series data, overcoming the limitations of insufficient training data and providing a more realistic and dynamic simulation of the financial market environment. By decomposing the data into distinct components, such as trend, dispersion, and residual, FED leverages pattern-centric data augmentation within the financial time series data. In the environment generated using the FED method, this paper proposes a two-class portfolio diversification, called FED2Port. It integrates stochastic elements into the reward function, enabling a reinforcement learning algorithm to learn from a comprehensive spectrum of financial market uncertainties. The experimental results demonstrate that the proposed model significantly enhances portfolio performance.

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H-(ϑ,φ)-contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems.

Power converters can convert the electrical energy output by power source into specific forms required by target device. They are widely used in various fields such as electrification, transportation, and power systems, and are the core components of the systems. Power converters are composed of power semiconductor devices (such as IGBTs), which are prone to failure due to abnormal conditions and aging degradation, leading to power converter faults. Therefore, over the past twenty years, extensive fault diagnosis methods for power converters have been studied and proposed. Among them, symmetry-based methods have the characteristics of rapid diagnosis speed and strong robustness, but so far there’s no systemic summary of such methods. Therefore, this paper reviews the relevant research on fault diagnosis of power converters based on symmetry in recent years, analyzes the mathematical principles of these methods, and compares their diagnostic performance. In addition, two factors that may have an influence on the symmetry are pointed out. This paper provides references and suggestions for the future development and research of power converter fault diagnosis.

In this article, the symmetric operator L corresponding to the boundary value problem is represented as the difference of two commuting operators A and B. The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required.

This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M,g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other geometrical features of l and (M,g). It is mainly a review of known material but contains some novelties. For example, the brief discussion of the nature of wave surfaces (when viewed geometrically as wave fronts to a null ray direction) in Wave Surfaces Section is new in the sense that although it appeared in the author’s work by the present author, it has not, to the best of his knowledge, appeared in this form anywhere else. Further, the work on conical symmetry and plane waves are, to the best of the author’s knowledge, original with him from earlier papers and are reviewed here while the work on complete wave surface (sectional curvature-) symmetry is believed to be entirely new. Geometrical use of the sectional curvature function is employed in many places. The consequences of the various symmetry conditions imposed on the collection of all wave surfaces to a null direction spanned by a null vector l are described in terms of l spanning a principal null direction of the Weyl tensor (if non-zero) at the point concerned (in the sense of Petrov and Bel).

Industrial control terminals play an important role in industrial control scenarios. Due to the special nature of industrial control networks, industrial control terminal systems are vulnerable to malicious attacks, which can greatly threaten the stability and security of industrial production environments. Traditional security protection methods for industrial control terminals have coarse detection granularity, and are unable to effectively detect and prevent attacks, lacking real-time responsiveness to attack events. Therefore, this paper proposes a real-time dynamic credibility evaluation mechanism based on program behavior, which integrates the matching and symmetry ideas of credibility evaluation. By conducting a real-time dynamic credibility evaluation of function call sequences and system call sequences during program execution, the credibility of industrial control terminal application program behavior can be judged. To solve the problem that the system calls generated during program execution are unstable and difficult to measure, this paper proposes a partition-based dynamic credibility evaluation method, dividing program behavior during runtime into function call behavior and system call behavior within function intervals. For function call behavior, a sliding window-based function call sequence benchmark library construction method is proposed, which matches and evaluates real-time measurement results based on the benchmark library, thereby achieving symmetry between the benchmark library and the measured data. For system call behavior, a maximum entropy system call model is constructed, which is used to evaluate the credibility of system call sequences. Experiment results demonstrate that our method performs better in both detection success rate and detection speed compared to the existing methods.

In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients |a2| and |a3| for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper.

Recently, transfer learning has gained popularity in the machine learning community. Transfer Learning (TL) has emerged as a promising paradigm that leverages knowledge learned from one or more related domains to improve prediction accuracy in a target domain with limited data. However, for time series forecasting (TSF) applications, transfer learning is relatively new. This paper addresses the need for empirical studies as identified in recent reviews advocating the need for practical guidelines for Transfer Learning approaches and method designs for time series forecasting. The main contribution of this paper is the suggestion of a comprehensive framework for Transfer Learning Sensitivity Analysis (SA) for time series forecasting. We achieve this by identifying various parameters seen from various angles of transfer learning applied to time series, aiming to uncover factors and insights that influence the performance of transfer learning in time series forecasting. Undoubtedly, symmetry appears to be a core aspect in the consideration of these factors and insights. A further contribution is the introduction of four TL performance metrics encompassed in our framework. These TL performance metrics provide insight into the extent of the transferability between the source and the target domains. Analyzing whether the benefits of transferred knowledge are equally or unequally accessible and applicable across different domains or tasks speaks to the requirement of symmetry or asymmetry in transfer learning. Moreover, these TL performance metrics inform on the possibility of the occurrence of negative transfers and also provide insight into the possible vulnerability of the network to catastrophic forgetting. Finally, we discuss a sensitivity analysis of an Ensemble TL technique use case (with Multilayer Perceptron models) as a proof of concept to validate the suggested framework. While the results from the experiments offer empirical insights into various parameters that impact the transfer learning gain, they also raise the question of network dimensioning requirements when designing, specifically, a neural network for transfer learning.

Developing appropriate signal timing strategies is a primary concern in traffic signal control; however, professionals are constrained by predefined controller options. Existing signal controllers in North America adhere to National Electrical Manufacturers Association (NEMA) standards with ring-barrier control (RBC) design. Due to unique traffic conditions and objectives for each traffic mode, conflicts arise, making it challenging to devise suitable traffic control strategies within current controllers. The limitations include inflexibility in defining pretimed signal diagrams, modifying them, and defining algorithms for modification. This paper introduces the event-based controller (EBC) framework, implemented in DUMKA_E software, capable of replicating NEMA-based RBC functionalities while providing additional flexibility beyond conventional RBC controllers. The EBC eliminates the asymmetry of flexibilities in existing traffic controller frameworks, addressing the challenges mentioned. Overcoming critical limitations of RBC, such as barrier constraints and restricted functionalities to built-in algorithms, the EBC empowers professionals to craft custom traffic signal control strategies. Unlike approaches enhancing RBC with complex computation, the EBC offers flexible functionalities without sacrificing simplicity. The study shows that the EBC’s fundamental concepts are no more intricate than RBC’s, positioning the EBC as a potential traffic controller framework. The paper establishes the EBC’s capability to reproduce RBC controllers’ core logic, showcasing advanced abilities for more efficient control logic than RBC. The EBC’s functionalities enable context-sensitive traffic signal control strategies, catering to special conditions like multi-modal activities and diverse priority requests, highlighting its full potential.

The properties of the unique nontrivial analytic solution, defined implicitly by a functional equation, are pointed out. This work provides local estimations and global inequalities for the involved solution. The corresponding operatorial equation is studied as well. The second part of the paper is devoted to the full classical moment problem, which is an inverse problem. Two constraints are imposed on the solution. One of them requires the solution to be dominated by a concrete convex operator defined on the positive cone of the domain space. A one-dimensional operator is valued, and a multidimensional scalar moment problem is solved. In both cases, the existence and the uniqueness of the solution are proved. The general idea of the paper is to provide detailed information on solutions which are not expressible in terms of elementary functions.

In Intelligent Transport Systems (ITSs), Internet of Vehicles (IoV) communications and computation offloading technology have been introduced to assist with the burdensome sensing task processing, thus prompting a new design paradigm called mobile sensing–communication–computation (MSCC) synergy. Most researchers have focused on offloading strategy design to reduce energy consumption or execution costs, but ignore the intrinsic characteristics of tasks, which may lead to poor performance. This paper studies the offloading strategy of vehicle MSCC tasks represented by a Directed Acyclic Graph (DAG) structure. According to the DAG dependency of the subtasks, this paper proposes a computation offloading strategy to optimize energy consumption under time constraints. An energy consumption model for task execution is established. Then, the Simulated Annealing and Tabu Search hybrid optimization algorithm (ST-HO) is designed to solve the problem of minimizing the energy consumption. Crucially, this research integrates the concept of symmetry into the typical DAG structure of MSCC tasks, ensuring the integrity and efficiency of task execution in ITS. The simulation results show that ST-HO reduces energy consumption by at least 5.58% compared to the conventional algorithm. Particularly, the convergence speed of ST-HO is improved by 52.63% when the replication strategy of symmetric task is considered.

Siamese trackers based on classification and regression have drawn extensive attention due to their appropriate balance between accuracy and efficiency. However, most of them are prone to failure in the face of abrupt motion or appearance changes. This paper proposes a Siamese-based tracker that incorporates spatial-semantic-aware attention and flexible spatiotemporal constraint. First, we develop a spatial-semantic-aware attention model, which identifies the importance of each feature region and channel to target representation through the single convolution attention network with a loss function and increases the corresponding weights in the spatial and channel dimensions to reinforce the target region and semantic information on the target feature map. Secondly, considering that the traditional method unreasonably weights the target response in abrupt motion, we design a flexible spatiotemporal constraint. This constraint adaptively adjusts the constraint weights on the response map by evaluating the tracking result. Finally, we propose a new template updating the strategy. This strategy adaptively adjusts the contribution weights of the tracking result to the new template using depth correlation assessment criteria, thereby enhancing the reliability of the template. The Siamese network used in this paper is a symmetric neural network with dual input branches sharing weights. The experimental results on five challenging datasets show that our method outperformed other advanced algorithms.

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on trajectory planning in autonomous ground vehicles (AGV), applying the traditional approach to dynamic traffic scenarios is inappropriate without considering vehicle dynamics environment and road regulations. This paper introduces a highly efficient approach for planning trajectories using improved artificial potential fields (IAPF) to handle dynamic road participants and address the issue of local minima in artificial potential fields. To begin with, potential fields are created with data obtained from other sensors. By incorporating rotational factors, the potential field will spin when the obstacle executes a maneuver; then, a safety distance model is also developed to limit the range of influence in order to minimize the computational burden. Furthermore, during the planning process, virtual forces using the gradient descent method are generated to direct the vehicle’s movement. During each timestep, the vehicle will assess whether it is likely to encounter a local minimum in the future. Once a local minimum is discovered, the method will create multiple temporary objectives to guide the vehicle toward the global minimum. Consequently, a trajectory that is both collision-free and feasible is planned. Traffic scenarios are carried out to validate the effectiveness of the proposed approach. The simulation results demonstrate that the improved artificial potential field approach is capable of generating a secure trajectory with both comfort and stability.

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper.

In the near future, the incorporation of shared electric automated and connected mobility (SEACM) technologies will significantly transform the landscape of transportation into a sustainable and efficient mobility ecosystem. However, these technological advances raise complex scientific challenges. Problems related to safety, energy efficiency, and route optimization in dynamic urban environments are major issues to be resolved. In addition, the unavailability of realistic and various data of such systems makes their deployment, design, and performance evaluation very challenging. As a result, to avoid the constraints of real data collection, using generated artificial datasets is crucial for simulation to test and validate algorithms and models under various scenarios. These artificial datasets are used for the training of ML (Machine Learning) models, allowing researchers and operators to evaluate performance and predict system behavior under various conditions. To generate artificial datasets, numerous elements such as user behavior, vehicle dynamics, charging infrastructure, and environmental conditions must be considered. In all these elements, symmetry is a core concern; in some cases, asymmetry is more realistic; however, in others, reaching/maintaining as much symmetry as possible is a core requirement. This review paper provides a comprehensive literature survey of the most relevant techniques generating synthetic datasets in the literature, with a particular focus on the shared electric automated and connected mobility context. Furthermore, this paper also investigates central issues of these complex and dynamic systems regarding how artificial datasets could be used in the training of ML models to address the repositioning problem. Hereby, symmetry is undoubtedly a crucial consideration for ML models. In the case of datasets, it is imperative that they accurately emulate the symmetry or asymmetry observed in real-world scenarios to be effectively represented by the generated datasets. Then, this paper investigates the current challenges and limitations of synthetic datasets, such as the reliability of simulations to the real world, and the validation of generative models. Additionally, it explores how ML-based algorithms can be used to optimize vehicle routing, charging infrastructure usage, demand forecasting, and other important operational elements. In conclusion, this paper outlines a series of interesting new research avenues concerning the generation of artificial data for SEACM systems.

Chirality and porosity are characteristic properties of nanostructured materials. Their effects on the mechanical behaviour of structural elements, such as shells, plates and beams, cannot be disregarded. In this paper, we study the thermoelastic deformation of a chiral porous circular beam loaded with an axial force and torque. The beam is also under the action of a constant temperature field. The analytical solution is obtained using the results established in a paper recently published by the Author within the context of the strain gradient theory proposed by Papanicopolous. In the constitutive equations, the chirality is introduced by a material constant parameter and the porosity is described by means of a scalar function. Displacements, microdilatation function, and stress and strain fields are expressed in explicit form and in terms of engineering constants. Explicit formulas of the stiffness of chiral porous circular beams are presented and the effects of right and left chirality are discussed.

In this paper, we discuss some extensions of the Maligranda–Orlicz lemma. It deals with the problem of constructing a norm in a subspace of the space of bounded functions, for which it becomes a normed algebra so that the norm introduced is equivalent to the initial norm of the subspace. This is done by satisfying some inequality between these norms. We show in this paper how this inequality is relevant to the study of operator equations in Banach algebras. In fact, we study how to equip a subspace of the space of bounded functions with a norm equivalent to a given one so that it is a normed algebra. We give a general condition for the construction of such norms, which allows us to easily check whether a space with a given norm is an algebra with a pointwise product and the consequences of such a choice for measures of noncompactness in such spaces. We also study quasi-normed spaces. We introduce a general property of measures of noncompactness that allows the study of quadratic operator equations, prove a fixed-point theorem suitable for such problems, and complete the whole with examples and applications.

New three-phase composite structures reinforced synergistically by nano-fillers and macroscopic fibers have great application potential. This paper presents a general framework for material properties calculation and the free vibration analysis of three-phase composite shell structures. Based on this methodological system, the free vibration characteristics of three types of nano-enhanced functionally graded three-phase composite cylindrical shells are investigated. First, the equivalent mechanical properties of these three three-phase composites were evaluated using the Halpin–Tsai and Mori–Tanaka models. The governing equations for the cylindrical shells were derived based on the first-order shear deformation theory (FSDT) and Hamilton’s principle. The equations were discretized using Galerkin’s method and solved to obtain the natural frequencies and mode shapes. The finite element simulation results and existing literature verified the accuracy and reliability of the method in this paper. The synergistic effects of nano-reinforced fillers and macroscopic fibers on the free vibrations of these structures were also analyzed. Among them, the natural frequency of the three-phase composite cylindrical shells was the highest when graphene platelets (GPLs) were used as the nano-reinforced fillers, which was 150.32% higher than that of fiber-reinforced epoxy composite cylindrical shells. These studies provide theoretical guidance for the design and manufacture of such symmetric or antisymmetric structures in the future.

Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection perpendicular to a single plane, projection images created by perpendicular projection onto two mutually perpendicular image planes, but placed on one plane, including the research of curves and movements, visual representation and perception relying on a mathematical approach, and studies on toothed driving pairs and tool geometry in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, for which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Our aim was to examine the spatial variation in the wear of the tool edge and the machining of the components of toothed drive pairs using two cameras. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the searching for the right projection direction, and positioning cameras appropriately. A special method of enumerating the possible infinite viewpoints for the reconstruction of tool surface edge curves is presented in the second part of this paper. In the case of the monitoring the shape geometry, taking into account the interchangeability of the projection directions, i.e., the property of symmetry, all images made from two perpendicular directions were taken into account. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. A new criterion was formulated for the tested tooth edge of the hob to take into account the shading of the tooth next to it. The analysis and some of the results of the Monge mapping, suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, namely defining the conditions for camera placements that ensure reconstructibility are also presented. Taking physical shadowing into account, conclusions can be drawn about the degree of distortion of the machined surface from the spatial deformation of the edge curve of the tool reconstructed with correctly positioned cameras.