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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.

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

The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

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.

Mathematical difficulty remains in many classical financial problems, especially for a closed-form expression of asset value. The European option evaluation problem based on a regime-switching has been formally modeled since early 2000, for which a recursive algorithm was developed to solve it. The key mathematical difficulty of this problem relies on the expectation IE[h(YT)], where h is a payoff function and {Yt}t∈[0,T] denotes a geometric Brownian motion with Markovian regime-switching. It is long since attempted to conclude this problem with closed form formulas. Towards the same target, this paper applies some novel techniques to draw explicit formulas for cases with more states for regime-switching (whereas the former deals the cases with two states) for any integrable function h (whereas the former only applies to the payoff of a European option). This paper combines the technique of occupation time of Markov chains and inverse Laplace transform to achieve the density function of geometric Brownian motion with Markovian regime-switching. Extension along this technique creates potential for probabilistic computations in addition to European option pricing. The reflection from the inverse Laplace transform to the expression of a moment-generating function is the core technique developed by this paper, and it is presented in symmetric forms.

Quality of Service (QoS) refers to techniques that function on a network to dependably execute high-priority applications and traffic reliably run high-priority applications and traffic even when the network’s capacity is limited. It is expected that data transmission over next-generation WSNs (Wireless Sensor Networks) 5G (5th generation) and beyond will increase significantly, especially for multimedia content such as video. Installing multiple IoT (Internet of Things refers to the network of devices that are all connected to each other) nodes on top of 5G networks makes the design more challenging. Maintaining a minimal level of service quality becomes more challenging as data volume and network density rise. QoS is critical in modern networks because it ensures critical performance metrics and improves end-user experience. Every client attempts to fulfill QoS access needs by selecting the optimal access device(s). Controllers will then identify optimum routes to meet clients’ core QoS needs in their core network. QoS-aware delivery is one of the most important aspects of wireless communications. Various models are proposed in the literature; however, an adaptive buffer size according to service type, priority, and incoming communication requests is required to ensure QoS-aware wireless communication. This article offers a hybrid end-to-end QoS delivery method involving customers and controllers and proposes a QoS-aware service delivery model for various types of communication with an adaptive buffer size according to the priority of the incoming service requests. For this purpose, this paper evaluates various QoS delivery models devised for service delivery in real time over IP networks. Multiple vulnerabilities are outlined that weaken QoS delivery in different models. Performance optimization is needed to ensure QoS delivery in next-generation WSN networks. This paper addresses the shortcomings of the existing service delivery models for real-time communication. An efficient queuing mechanism is adopted that assigns priorities based on input data type and queue length. This queuing mechanism ensures QoS efficiency in limited bandwidth networks and real-time traffic. The model reduces the over-provisioning of resources, delay, and packet loss ratio. The paper contributes a symmetrically-designed traffic engineering model for QoS-ensured service delivery for next-generation WSNs. A dynamic queuing mechanism that assigns priorities based on input data type and queue length is proposed to ensure QoS for wireless next-generation networks. The proposed queuing mechanism discusses topological symmetry to ensure QoS efficiency in limited bandwidth networks with real-time communication. The experimental results describe that the proposed model reduces the over-provisioning of resources, delay, and packet loss ratio.

The additive hazard regression model plays an important role when the excess risk is the quantity of interest compared to the relative risks, where the proportional hazard model is better. This paper discusses parametric regression analysis of survival data using the additive hazards model with competing risks in the presence of independent right censoring. In this paper, the baseline hazard function is parameterized using a modified Weibull distribution as a lifetime model. The model parameters are estimated using maximum likelihood and Bayesian estimation methods. We also derive the asymptotic confidence interval and the Bayes credible interval of the unknown parameters. The finite sample behaviour of the proposed estimators is investigated through a Monte Carlo simulation study. The proposed model is applied to liver transplant data.

Integral inequalities concerned with convexity have many applications in several fields of mathematics in which symmetry plays an important role. In the theory of convexity, there exist strong connections between convexity and symmetry. If we are working on one of the concepts, then it can be applied to the other of them. In this paper, we establish some novel generalizations of Ostrowski type inequalities for exponentially s-preinvex and s-preinvex functions on time scale by using Hölder inequality and Montgomery Identity. We also obtain applications to some special means. These results are motivated by the symmetric results obtained in the recent article by Abbasi and Anwar in 2022 on Ostrowski type inequalities for exponentially s-convex functions and s-convex functions on time scale. Moreover, we discuss several special cases of the results obtained in this paper.

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use k-means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers’ evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai “6.18” Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper.

(1) Background: In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. (2) Methods: We use standard physical theories such as Maxwell electrodynamics and quantum mechanics, supplemented by tools from vector analysis and numerics. (3) Results: We show that a hydrogen atom either in the ground state or excited state will not produce a relativistic engine effect, but by breaking the symmetry or putting the electron in a wave packet state may produce relativistic motor effect. (4) Conclusions: A highly localized wave packet will produce a strong relativistic motor effect. The preliminary analysis of the current paper suggests new promising directions of research both theoretical and experimental.

Most existing Siamese trackers mainly use a pre-trained convolutional neural network to extract target features. However, due to the weak discrimination of the target and background information of pre-trained depth features, the performance of the Siamese tracker can be significantly degraded when facing similar targets or changes in target appearance. This paper proposes a multi-channel-aware and adaptive hierarchical deep features module to enhance the discriminative ability of the tracker. Firstly, through the multi-channel-aware deep features module, the importance values of feature channels are obtained from both the target details and overall information, to identify more important feature channels. Secondly, by introducing the adaptive hierarchical deep features module, the importance of each feature layer can be determined according to the response value of each frame, so that the hierarchical features can be integrated to represent the target, which can better adapt to changes in the appearance of the target. Finally, the proposed two modules are integrated into the Siamese framework for target tracking. The Siamese network used in this paper is a two-input branch symmetric neural network with two input branches, and they share the same weights, which are widely used in the field of target tracking. Experiments on some Benchmarks show that the proposed Siamese tracker has several points of improvement compared to the baseline tracker.

Multiphoton Quantum Key Distribution (QKD) has recently been proposed to exchange the secret keys using the rotational of polarization over a multi-stage protocol. It has the ability to outperform the weaknesses of a single photon QKD by improving the generation of key rate and distance range. This paper investigates the theoretical aspects of multiphoton QKD protocol&rsquo, s performance over free space optic (FSO) networks. The most common setup for quantum communication is the single-beam approach. However, the single-beam setup has limitations in terms of high geometrical loss. In this paper, the symmetry multiple-beam for quantum communication which is called as Multiphoton Quantum Communication-Multiple Beam (MQC-MB) is proposed to transmit the multiphoton from the sender to the receiver in order to minimize the impact of geometrical loss that is faced by the single-beam setup. The analysis was carried out through mathematical analysis by establishing the FSO quantum model with the effects of atmospheric and geometrical loss as well as considering atmospheric turbulence modeled by log-normal distribution. The design criteria of FSO, such as the transmitter, receiver, beam divergence, and diameter of apertures, are analytically investigated. The numerical results demonstrate that the MQC-MB outperforms the single-beam in terms of reducing channel loss by about 8 dB and works well under strong turbulence channel. Furthermore, the MQC-MB reduces the quantum bit error rate (QBER) and improves the secret key rate (SKR) as compared to the single-beam system even though the distance between the sender and receiver increases.

Automatic segmentation of intracranial brain tumors in three-dimensional (3D) image series is critical in screening and diagnosing related diseases. However, there are various challenges in intracranial brain tumor images: (1) Multiple brain tumor categories hold particular pathological features. (2) It is a thorny issue to locate and discern brain tumors from other non-brain regions due to their complicated structure. (3) Traditional segmentation requires a noticeable difference in the brightness of the interest target relative to the background. (4) Brain tumor magnetic resonance images (MRI) have blurred boundaries, similar gray values, and low image contrast. (5) Image information details would be dropped while suppressing noise. Existing methods and algorithms do not perform satisfactorily in overcoming these obstacles mentioned above. Most of them share an inadequate accuracy in brain tumor segmentation. Considering that the image segmentation task is a symmetric process in which downsampling and upsampling are performed sequentially, this paper proposes a segmentation algorithm based on U-Net++, aiming to address the aforementioned problems. This paper uses the BraTS 2018 dataset, which contains MR images of 245 patients. We suggest the generative mask sub-network, which can generate feature maps. This paper also uses the BiCubic interpolation method for upsampling to obtain segmentation results different from U-Net++. Subsequently, pixel-weighted fusion is adopted to fuse the two segmentation results, thereby, improving the robustness and segmentation performance of the model. At the same time, we propose an auto pruning mechanism in terms of the architectural features of U-Net++ itself. This mechanism deactivates the sub-network by zeroing the input. It also automatically prunes GenU-Net++ during the inference process, increasing the inference speed and improving the network performance by preventing overfitting. Our algorithm’s PA, MIoU, P, and R are tested on the validation dataset, reaching 0.9737, 0.9745, 0.9646, and 0.9527, respectively. The experimental results demonstrate that the proposed model outperformed the contrast models. Additionally, we encapsulate the model and develop a corresponding application based on the MacOS platform to make the model further applicable.

In this paper, we proposed a scheme that Injects artificial noise from the tag end (IANT) to enhance the physical layer security of the ambient backscatter communication (ABC) system. The difference between the ABC system and the traditional radio frequency identification system is whether it uses the radio frequency (RF) signals in the environment to supply energy and modulation information for passive tags. In the IANT scheme, we select the best tag to communicate with the reader according to the channel quality between tags and reader, and at the same time select another tag to generate artificial noise that affects the receiving effect of the eavesdropper. This paper uses the method of generating noise copies in the reader to reduce the interference of artificial noise on the signal received by the reader. The simulation results show that with the increase in channel quality between tags and reader and the increase in the number of tags, the proposed IANT scheme is significantly superior to the contrast scheme in terms of system achievable secrecy rate, effectively enhancing the physical layer security of the ABC system.

Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means, using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. We explore certain convex or concave functions, which are symmetric functions on the axis t=1/2.

This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we study some integrable properties for this system such as Hamiltonian structures, Liouville integrability and conservation laws. Secondly, we construct a discrete generalized (m,2N−m)-fold Darboux transformation based on its known Lax pair. Thirdly, we obtain some exact solutions including soliton, rational and semi-rational solutions with arbitrary controllable parameters and hybrid solutions by using the resulting Darboux transformation. Finally, in order to understand the properties of such solutions, we investigate the limit states of the diverse exact solutions by using graphic and asymptotic analysis. In particular, we discuss the asymptotic states of rational solutions and exponential-and-rational hybrid solutions graphically for the first time, which might be useful for understanding the motions of particles in lattices. Numerical simulations are used to discuss the dynamics of some soliton solutions. The results and properties provided in this paper may enrich the understanding of nonlinear lattice dynamics.

A cable-stayed bridge is a typical symmetrical structure, and symmetry affects the deformation characteristics of such bridges. The main girder of a cable-stayed bridge will produce obvious deflection under the inducement of temperature. The regression model of temperature-induced deflection is hoped to provide a comparison value for bridge evaluation. Based on the temperature and deflection data obtained by the health monitoring system of a bridge, establishing the correlation model between temperature and temperature-induced deflection is meaningful. It is difficult to complete a high-quality model only by the girder temperature. The temperature features based on prior knowledge from the mechanical mechanism are used as the input information in this paper. At the same time, to strengthen the nonlinear ability of the model, this paper selects an independent recurrent neural network (IndRNN) for modeling. The deep learning neural network is compared with machine learning neural networks to prove the advancement of deep learning. When only the average temperature of the main girder is input, the calculation accuracy is not high regardless of whether the deep learning network or the machine learning network is used. When the temperature information extracted by the prior knowledge is input, the average error of IndRNN model is only 2.53%, less than those of BPNN model and traditional RNN. Combining knowledge with deep learning is undoubtedly the best modeling scheme. The deep learning model can provide a comparison value of bridge deformation for bridge management.

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.

This paper is devoted to further strengthening, in the current asymmetric information environment, the informed level of operators about network performance. Specifically, in view of the burst and perishability of a packet loss event, to better meet the real-time requirements of current high-speed backbone performance monitoring, a model for Packet Loss Measurement at the access network boundary Based on Sampled Flow (PLMBSF) is presented in this paper under the premise of both cost and real-time. The model overcomes problems such as the inability of previous estimation to distinguish between packet losses before and after the monitoring point, deployment difficulties and cooperative operation consistency. Drawing support from the Mathis equation and regression analysis, the measurement for packet losses before and after the monitoring point can be realized when using only the sampled flows generated by the access network boundary equipment. The comparison results with the trace-based passive packet loss measurement show that although the proposed model is easily affected by factors such as flow length, loss rate, sampling rate, the overall accuracy is still within the acceptable range. In addition, the proposed model PLMBSF, compared with the trace-based loss measurement is only different in the input data granularity. Therefore, PLMBSF and its advantages are also applicable to aggregated traffic.

Recently in the paper [Mediterr. J. Math.&nbsp, 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.

The paper aims to analyze the vibrations of a summing box, used in heavy vehicles. An experimental setup is proposed and used for the analysis of these vibrations transmitted by the box housing, based on the measurement of the mechanical impedance. It is then shown that a simpler measurement, namely that of the generated noise spectrum, can provide equally useful results, with less effort and in a shorter time. The experimental setup is much simpler, involving a sonometer arranged in the experimental assembly. The symmetry of the box allows us to facilitate the execution of the experimental assembly, and the use of the symmetrical structure to facilitate the calculation of vibrations. The results obtained using this method in the case of a redesigned adder box are presented in the paper.

Most of the papers published so far in literature have focused on the theoretical phenomena underlying the formation of chaos, rather than on the investigation of potential applications of chaos to the real world. This paper aims to bridge the gap between chaos theory and chaos applications by presenting a survey of very recent applications of chaos. In particular, the manuscript covers the last three years by describing different applications of chaos as reported in the literature published during the years 2018 to 2020, including the matter related to the symmetry properties of chaotic systems. The topics covered herein include applications of chaos to communications, to distributed sensing, to robotic motion, to bio-impedance modelling, to hardware implementation of encryption systems, to computing and to random number generation.

Increasingly, cities worldwide are striving for green travel and slow traffic, and vigorously developing people-oriented urban pedestrian traffic with sustainability has become a fixture in recent discourse. This paper comprehensively considers the sidewalk’s facilities environment and the status of pedestrian traffic flow; divides the urban pedestrian road system (UPRS) into five subsystems around the underpass, overpass, crosswalk, sidewalk, and road crosswalk; and introduces the basic structure as well as the function of each system. Then, the indicators are classified into two types of crosswalk facilities and sidewalk facilities, and a comprehensive pedestrian road indicator system with the combination of subjective and objective is established. Consequently, the integration of the fuzzy AHP and DEA-based symmetrical technique for the subjective evaluation indicator combined with pedestrian traffic characteristics is developed. A nine-step semantics scale of relative importance was used so that the symmetry of the response of pedestrian satisfaction was maintained. Fuzzy evaluation based on AHP is further modeled, and the DEA is employed to achieve an overall evaluation of the quality of service (QoS) for UPRS. The applicability of the established evaluation system is finally verified through a real case study in Harbin, China. The serviceability assessment method in this paper provides a new idea for planners to conduct sustainability evaluation for UPRS in future urban renewal development.

A review of experimental studies carried out at the NRC “Kurchatov Institute” on plasma-facing thermonuclear fusion reactor materials is presented in the paper. An experimental method was developed to produce high-level radiation damage in materials simulating the neutron effect by surrogate irradiation with high-energy ions. Plasma-surface interaction is investigated on materials irradiated to high levels of radiation damage in high-flux deuterium plasma. The total fluence of accelerated ions (3–30 MeV, 4He2+, 12C3+, 14N3+, protons) on the samples was 1021–1023 m−2. Experiments were carried out on graphite materials, tungsten, and silicon carbide. Samples have been obtained with a primary defect concentration from 0.1 to 100 displacements per atom, which covers the predicted damage for the ITER and DEMO projects. Erosion dynamics of the irradiated materials in steady-state deuterium plasma, changes of the surface microstructure, and deuterium retention were studied using SEM, TEM, ERDA, TDS, and nuclear backscattering techniques. The surface layer of the materials (3 to hundreds µm) was investigated, and it was shown that the changes in the crystal structure, the loss of their symmetry, and diffusion of defects to grain boundaries play an important role. The most significant results are presented in the paper as an overview of our previous work for many years (carbon and tungsten materials) as well as the relatively recent results (silicon carbide).

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings.

This paper studies the multi-depot joint distribution vehicle routing problem considering energy consumption with time-dependent networks (MDJDVRP-TDN). Aiming at the multi-depot joint distribution vehicle routing problem where the vehicle travel time depends on the variation characteristics of the road network speed in the distribution area, considering the influence of the road network on the vehicle speed and the relationship between vehicle load and fuel consumption, a multi-depot joint distribution vehicle routing optimization model is established to minimize the sum of vehicle fixed cost, fuel consumption cost and time window penalty cost. Traditional vehicle routing problems are modeled based on symmetric graphs. In this paper, considering the influence of time-dependent networks on routes optimization, modeling is based on asymmetric graphs, which increases the complexity of the problem. A hybrid genetic algorithm with variable neighborhood search (HGAVNS) is designed to solve the model, in which the nearest neighbor insertion method and Logistic mapping equation are used to generate the initial solution firstly, and then five neighborhood structures are designed to improve the algorithm. An adaptive neighborhood search times strategy is used to balance the diversification and depth search of the population. The effectiveness of the designed algorithm is verified through several groups of numerical instances with different scales. The research can enrich the relevant theoretical research of multi-depot vehicle routing problems and provide the theoretical basis for transportation enterprises to formulate reasonable distribution schemes.

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group of the rigid body displacements, SE3. We obtain a simplified form of the initial value problem that models the non-inertial motion using a tensor instrument introduced in this paper. Thus, the study of the motion in a non-inertial reference frame is transferred into the study of a classical motion in an inertial reference frame. The applications of this method refer to solving the relative motion problem and deriving the straightforward solution to classical theoretical mechanics problems. The motion in a uniform gravitational force field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, the exact solution of the relative rigid body motion in the non-inertial reference frame are studied. Using this symbolic method in studying the motion in a non-inertial reference frame reduces the number of computations. In addition, it offers, in some essential particular cases, exact closed-form coordinate-free analytical solutions.

The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

In order to play the important role of electric vehicles to promote the realization of the 3060 double carbon target, electric vehicles have seen explosive growth. However, due to the tight symmetry between the number and distribution of electric vehicles and their corresponding charging facilities, the layout of charging facilities has higher requirements. This paper collects travel data in the form of a traffic travel questionnaire for electric vehicle users. Based on the vehicle parking demand model of the queuing theory and Monte Carlo simulation, the paper gives the number of stopping vehicles and the time of vehicles stopping in different places such as residential areas, workplaces, supermarket parking and roadside. In addition, based on the Bass prediction model, the main parameters are modeled in the model, and the price correction coefficient is introduced. The improved Bass model is used to predict the growth trend of electric vehicles in different regions in different years and in different incentive sites. By predicting the ownership of urban electric vehicles and accurately grasping the distribution and operation of electric vehicles, this paper can provide guidance and suggestions for the planning and construction of charging facilities in different regions, effectively reduce the investment cost of charging facilities and guide local governments to formulate reasonable planning schemes.

Based on the current background of airport management and flight-gate scheduling in China, this paper takes Shanghai Pudong International Airport’s flight number of the rising and landing aircraft in a certain day as the research object, and it establishes an uncertain FGAP (Flight-Gate Assignment Problem) multi-objective programming model under the framework of uncertainty theory. Using genetic algorithm to solve the model, the specific flight-gate assignment scheduling plan is given. The research results show that the model in this paper can effectively alleviate the problems, such as unbalanced flight-gate allocation and excessive operating pressure of a single gate, in the conventional model, and make the allocation and scheduling more reasonable and efficient. Finally, we give the future application of uncertainty theory in finance and management, as well as the prospect of combining it with symmetry in physics.

In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite–Hadamard type via Hölder’s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.

The implications of the end effect for flux linkage and thrust ripple in a slot-less long-stator permanent magnet linear synchronous motor (LSPMLSM), are analyzed in this paper. Since it is affected by the end effect, the air-gap magnetic field density under the end permanent magnet is different from that under the non-end permanent magnet, leading to asymmetry in the thrust ripple. For this reason, we establish a dynamic permanent magnet flux linkage model, which proves that the end effect leads to sub-harmonics in the permanent magnet flux linkage. The motor’s magnetic field distribution in the left and right parts is symmetrical. A thrust model taking into account the flux linkage sub-harmonics is established, from which the amplitude and period of the thrust ripple caused by the end effect can be calculated. There is no detent force for the slot-less LSPMLSM, and the end effect is the primary origin of the motor thrust ripple. In order to suppress the end effect, a method of increasing the end iron length is proposed, as a result of which the sub-harmonics in the flux linkage and the motor thrust ripple are effectively suppressed. Experimental and simulation results verify the results of this paper.

The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring. The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring.

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density, thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions, a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

Class imbalance, as a phenomenon of asymmetry, has an adverse effect on the performance of most machine learning and overlap is another important factor that affects the classification performance of machine learning algorithms. This paper deals with the two factors simultaneously, addressing the class overlap under imbalanced distribution. In this paper, a theoretical analysis is firstly conducted on the existing class overlap metrics. Then, an improved method and the corresponding metrics to evaluate the class overlap under imbalance distributions are proposed based on the theoretical analysis. A well-known collection of the imbalanced datasets is used to compare the performance of different metrics and the performance is evaluated based on the Pearson correlation coefficient and the ξ correlation coefficient. The experimental results demonstrate that the proposed class overlap metrics outperform other compared metrics for the imbalanced datasets and the Pearson correlation coefficient with the AUC metric of eight algorithms can be improved by 34.7488% in average.

Conjectures on permanents are well-known unsettled conjectures in linear algebra. Let A be an n×n matrix and Sn be the symmetric group on n element set. The permanent of A is defined as perA=∑σ∈Sn∏i=1naiσ(i). The Merris conjectured that for all n×n doubly stochastic matrices (denoted by Ωn), nperA≥min1≤i≤n∑j=1nperA(j|i), where A(j|i) denotes the matrix obtained from A by deleting the jth row and ith column. Foregger raised a question whether per(tJn+(1−t)A)≤perA for 0≤t≤nn−1 and for all A∈Ωn, where Jn is a doubly stochastic matrix with each entry 1n. The Merris conjecture is one of the well-known conjectures on permanents. This conjecture is still open for n≥4. In this paper, we prove the Merris inequality for some classes of matrices. We use the sub permanent inequalities to prove our results. Foregger’s inequality is also one of the well-known inequalities on permanents, and it is not yet proved for n≥5. Using the concepts of elementary symmetric function and subpermanents, we prove the Foregger’s inequality for n=5 in [0.25, 0.6248]. Let σk(A) be the sum of all subpermanents of order k. Holens and Dokovic proposed a conjecture (Holen–Dokovic conjecture), which states that if A∈Ωn,A≠Jn and k is an integer, 1≤k≤n, then σk(A)≥(n−k+1)2nkσk−1(A). In this paper, we disprove the conjecture for n=k=4.

The mutual confrontation between image steganography and steganalysis causes both to iterate continuously, and as a result, the dimensionality of the steganalytic features continues to increase, leading to an increasing spatio-temporal overhead. To this end, this paper proposes a fast steganalytic feature selection method based on a similar cross-entropy. Firstly, the properties of cross-entropy are investigated, through the discussion of different models, and the intra-class similarity criterion and inter-class similarity criterion based on cross-entropy are presented for the first time. Then, referring to the design principles of Fisher’s criterion, the criterion of feature contribution degree is further proposed. Secondly, the variation of the cross-entropy function of a univariate variable is analyzed in principle, thus determining the normalized range and simplifying the subsequent analysis. Then, within the normalized range, the variation of the cross-entropy function of a binary variable is investigated and the setting of important parameters is determined. Thirdly, the concept of similar cross-entropy is further presented by analyzing the changes in the value of the feature contribution measure under different circumstances, and based on this, the criterion for the feature contribution measure is updated to decrease the complexity of the calculation. Remarkably, the contribution measure criterion devised in this paper is a symmetrical structure, which equitably measures the contribution of features in different situations. Fourth, the feature component with the highest contribution is selected as the final selected feature based on the result of the feature metric. Finally, based on the Bossbase 1.01 image base that is a unique standard and recognized base in steganalysis, the feature selection on 8 kinds of low and high-dimensional steganalytic features is carried out. Through extensive experiments, comparison with several classic and state-of-the-art methods, the method designed in this paper attains competitive or even better performance in detection accuracy, calculation cost, storage cost and versatility.

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups are vanishing, and M3 is homotopic to the Euclidean sphere S3 under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds.

In this paper, the dynamic characteristics of sandwich plates with external rigid layers and an upper layer with magnetorheological properties (MR) are investigated. An analysis of the effect of the magnetic field on frequency and loss factor is presented. Vibration can be controlled by a magnetic-rheological viscoelastomer (MRVE), when used in sandwich plates. During vibration, MRVE exhibits an inhomogeneous complex module, which is controlled by an applied magnetic field and depends on the oscillation frequency. Using the dynamic equilibrium conditions, physical and kinematic relationships, and the partial differential equations for the conjugate transverse and longitudinal oscillations of a sandwich plate, are derived. This paper presents a new method for stress analysis that provides accurate stress distributions for multilayer plates subject to cylindrical bending. It uses an adaptive method that does not make strict assumptions about the plate model. Based on the depicted theoretical model, the deformations of each layer of the plate are accounted for, including both transverse shear deformations and transverse normal deformations where the thickness is concerned, and nonlinear displacement changes. The magnetorheological (MR) identification of an inner layer is carried out using refined plate theory and sandwich bending tests. Using combined methods, the possibility of determining the MRVE parameters robustly, is examined.

In the years 1917–1919 Tullio Levi-Civita published a number of papers presenting new solutions to Einstein’s equations. This work, while partially translated, remains largely inaccessible to English speaking researchers. In this paper we review these solutions, and present them in a modern readable manner. We will also compute both Cartan–Karlhede and Carminati–Mclenaghan invariants such that these solutions are invariantly characterized by two distinct methods. These methods will allow for these solutions to be totally and invariantly characterized. Because of the variety of solutions considered here, this paper will also be a useful reference for those seeking to learn to apply the Cartan–Karlhede algorithm in practice.