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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 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.

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.

This paper looks at the problem of cybersecurity in modern cyber-physical and information systems and proposes an immune-like approach to the information security of modern complex systems. This approach is based on the mathematical modeling in information security—in particular, the use of immune methods to protect several critical system nodes from a predetermined range of attacks, and to minimize the success of an attack on the system. The methodological approach is to systematize the tasks, means and modes of immunization to describe how modern systems can counter the spread of computer attacks. The main conclusions and recommendations are that using an immunization approach will not only improve the security of systems, but also define principles for building systems that are resistant to cyber attacks. The immunization approach enables a symmetrical response to an intruder in a protected system to be produced rapidly. This symmetry provides a step-by-step neutralization of all stages of a cyber attack, which, combined with the accumulation of knowledge of the attacker’s actions, allows a base of defensive responses to be generated for various cyber attack scenarios. The theoretical conclusions are supported by practical experiments describing real-world scenarios for the use of immunization tools to protect against cyber threats.

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of b−metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of b−metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β&gt, 0.02, −0.06&lt, β&lt, 0.02 and β&lt, −0.06. The influence rules and some interesting phenomena are investigated.

Over the last two decades (2000–2020), the Internet has rapidly evolved, resulting in symmetrical and asymmetrical Internet consumption patterns and billions of users worldwide. With the immense rise of the Internet, attacks and malicious behaviors pose a huge threat to our computing environment. Brute-force attack is among the most prominent and commonly used attacks, achieved out using password-attack tools, a wordlist dictionary, and a usernames list—obtained through a so-called an enumeration attack. In this paper, we investigate username enumeration attack detection on SSH protocol by using machine-learning classifiers. We apply four asymmetrical classifiers on our generated dataset collected from a closed-environment network to build machine-learning-based models for attack detection. The use of several machine-learners offers a wider investigation spectrum of the classifiers’ ability in attack detection. Additionally, we investigate how beneficial it is to include or exclude network ports information as features-set in the process of learning. We evaluated and compared the performances of machine-learning models for both cases. The models used are k-nearest neighbor (K-NN), naïve Bayes (NB), random forest (RF) and decision tree (DT) with and without ports information. Our results show that machine-learning approaches to detect SSH username enumeration attacks were quite successful, with KNN having an accuracy of 99.93%, NB 95.70%, RF 99.92%, and DT 99.88%. Furthermore, the results improve when using ports information.

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.

The present research paper considers a three-level atom (3LA) that interacts with a field mode primarily in a photon-added coherent state of Morse potential (PACSMP). The dynamics of entanglement, the photon statistics, and the quantum Fisher information are investigated. The statistics of field photons are discussed by evaluating the Mandel parameter. We check the influence of the energy dissipation and intensity-dependent function. Finally, we detect the relationship between the entanglement, the field’s nonclassical characteristics, and atomic quantum Fisher information throughout the evolution of time. The findings illustrate the important role of the number of added photons and CSMP in affecting the entanglement’s time evolution, the quantum Fisher information, and the Mandel parameter. Based on the obtained results, we reached significant physical phenomena, including the sudden birth and death of the nonlocal correlation between atom-Morse potential field structures.

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given, one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value, therefore, it is worth trying to use combination therapy to treat HCV infection.

In traditional cloud computing research, it is often considered that the network resources between edge devices and cloud platform are sufficient, and the symmetry between the upward link from edge devices to the cloud platform and the downward link from cloud platform to edge devices is definite. However, in many application scenarios, the network resources between edge devices and cloud platform might be limited, and the link symmetry may not be guaranteed. To solve this problem, network relay nodes are introduced to realize the data transmission between edge devices and the cloud platform. The environment in which network relay nodes that can cooperate with the cloud platform is called cloud network collaborative environment (CNCE). In CNCE, how to optimize data transmission from edge devices to cloud platform through relay nodes has become one of the most important research topics. In this paper, we focus on the following two influencing factors that previous studies ignored: (1) the multi-link and multi-constraint transmission process, and (2) the timely resource state of the relay node. Taking these factors into consideration, we design a novel data transmission scheduling algorithm, called ant colony based transmission scheduling approach (ACTS). First, we propose a multi-link optimization mechanism to optimize the constraint limits. This mechanism divides the transmission into two links called the downlink relay link and uplink relay link. For the downlink relay link, we use the store-and-forward method for the optimization. For the uplink relay link, we use the min–min method for the optimization. We use the ant colony algorithm for the overall optimization of the two links. Finally, we improve the pheromone update rule of the ant colony algorithm to avoid the algorithm from falling into a local optimum. Extensive experiments demonstrate that our proposed approach has better results in transmission efficiency than other advanced algorithms.

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.

This paper presents several types of Johnson–Tzitzeica theorems. Graph diagrams are used in this analysis. A symmetric scheme is derived, and new results are obtained and open problems stated. We also present results relating the graphs and the Yang–Baxter equation. This equation has certain symmetries, which are used in finding solutions for it. All these constructions are related to integrable systems.

This paper presents a robust nonlinear control scheme with time-varying output constraint for the electro-hydraulic force control system (EHFCS). Two typical double-rod symmetrical hydraulic cylinders are employed to simulate force environments in the EHFCS. Therefore, in order to improve the performance of the EHFCS, firstly, the model of the EHFCS is established with taking external disturbances, parameter uncertainties as well as structural vibrations into consideration. Secondly, in order to estimate external disturbances, parameter uncertainties and structural vibrations in the EHFCS and compensate them in the following robust controller design, two disturbance observers (DOs) are designed according to the nonlinear system model. Thirdly, with two estimation values from two DOs, a time-varying constraint-based robust controller (TVCRC) is presented in detail. Moreover, the stability of the proposed controller is analyzed by defining a proper Lyapunov functions. Finally, in order to validate the performance of the proposed controller, a series of simulation studies are conducted using the MATLAB/Simulink software. These simulation results give a fine proof of the efficiency of the proposed controller. What’s more, an experimental setup of the EHFCS is established to further validate the performance. Comparative experimental results show that the proposed controller exhibits better performance than the TVCRC without two DOs and a conventional proportional integral (PI) controller.

Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,…,ak}, where a1,a2,a3,…,ak are k distinct elements in Z(R,k), which means (i) a1a2a3⋯ak=0 and (ii) the products of all elements of any (k−1) subsets of {a1,a2,a3,…,ak} are nonzero. This paper provides two commutative rings so that one of them induces a family of complete k-zero-divisor hypergraphs, while another induces a family of k-partite σ-zero-divisor hypergraphs, which illustrates unbalanced or asymmetric structure. Moreover, the diameter and the minimum length of all cycles or girth of the family of k-partite σ-zero-divisor hypergraphs are determined. In addition to a k-zero-divisor hypergraph, we provide the definition of an ideal-based k-zero-divisor hypergraph and some basic results on these hypergraphs concerning a complete k-partite k-uniform hypergraph, a complete k-uniform hypergraph, and a clique.

Expert systems, a form of artificial intelligence (AI), are typically designed to solve many real-world problems by reasoning through knowledge, which is primarily represented as IF–THEN rules, with the information acquired from humans or domain experts. However, to assume such rules for personalized decision-making in an intelligent, context-aware mobile application is a challenging issue. The reason is that different mobile users may behave differently in various day-to-day situations, i.e., not identical, and thus the rules for personalized services must be reflected according to their symmetrical or asymmetrical behavioral activities. Therefore, our key focus is to solve this issue through adding personalized decision-making intelligence to develop powerful mobile applications to assist the end-users. To achieve our goal, in this paper, we explore on “Mobile Expert System”, where we take into account machine-learning rules as knowledge-base rather than traditional handcrafted static rules. Thus, the concept of a mobile expert system enables the computing and decision-making processes more actionable and intelligent than traditional ones in the domain of mobile analytics and applications. Our experiment section shows that the context-aware machine learning rules discovered from users’ mobile phone data can contribute in building a mobile expert system to solve a particular problem, through making personalized decisions in various context-aware test cases.

Navarro et al. (2010) proposed the increasing dynamic cumulative past entropy (IDCPE) class of life distributions. In this paper, we investigate some characterizations of this class. Closure and reversed closure properties of the IDCPE class are obtained. As applications of a main result, we explore the preservation and reversed preservation properties of this class in several stochastic models. We also investigate preservation and reversed preservation of the IDCPE class for coherent systems with dependent and identically distributed components.

In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice.

Plastic anisotropy significantly influences the behavior of structures subjected to various loading conditions. The extremum principles in the theory of rigid plastic solids are convenient and reliable tools for plastic design. The present paper combines the upper bound theorem and Hill’s quadratic yield criterion for orthotropic materials to evaluate the plastic collapse load of a highly undermatched welded tensile panel with a crack in the weld. The base material is supposed to be rigid. The shape of the crack is quite arbitrary. The orientation of the principal axes of anisotropy varies through the thickness of the weld. The upper bound solution is based on an exact solution for a layer of an anisotropic material. This feature of the upper bound solution is advantageous for increasing its accuracy. A numerical treatment is only necessary to find the solution for the uncracked specimen. This specimen has two axes of symmetry, which simplifies the solution. Simple analytic formulae transform this solution into a solution for the cracked specimens with one axis of symmetry and no symmetry. It is shown that the through-thickness distribution of anisotropic properties significantly affects the limit load.

This research paper is dedicated to the study of a class of boundary value problems for a nonlinear, implicit, hybrid, fractional, differential equation, supplemented with boundary conditions involving general fractional derivatives, known as the ϑ-Hilfer and ϑ-Riemann–Liouville fractional operators. The existence of solutions to the mentioned problem is obtained by some auxiliary conditions and applied Dhage’s fixed point theorem on Banach algebras. The considered problem covers some symmetry cases, with respect to a ϑ function. Moreover, we present a pertinent example to corroborate the reported results.

This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.

With the rapid increase of volume and complexity in the projectile flight test business, it is becoming increasingly important to improve the quality of the service and efficiency of multi-domain cooperative networks. The key for these improvements is to solve the problem of asymmetric load of multi-controllers in multi-domain networks. However, due to the current reality, it is difficult to meet the demands of future tests, and there is not guarantee of subnet multi-domain test load balancing. Most recent works have used a heuristic approach to seek the optimal dynamic migration path, but they may fall into the local optimum. This paper proposes an improved ant colony algorithm (IACO) that can transform the modeling of the mapping relationship between the switch and the controller into a traveling salesman problem by combining the ant colony algorithm and artificial fish swarm algorithm. The IACO not only ensures the load balancing of multi-controllers but also improves the reliability of the cluster. The simulation results show that compared to other algorithms such as traditional ant colony algorithms and distributed decision mechanisms, this IACO achieves better load balancing, improves the average throughput of multi-controller clusters, and effectively reduces the response time of controller request events.

For the analysis of square contingency tables with ordered categories, a measure was developed to represent the degree of departure from the conditional symmetry model in which there is an asymmetric structure of the cell probabilities with respect to the main diagonal of the table. The present paper proposes a novel measure for the departure from conditional symmetry based on the cumulative probabilities from the corners of the square table. In a given example, the proposed measure is applied to Japanese occupational status data, and the interpretation of the proposed measure is illustrated as the departure from a proportional structure of social mobility.

When decision making units (DMUs) have internal structures with imprecise inputs and outputs, uncertain network data envelopment analysis (UNDEA) is appropriate to deal with the efficiency evaluation of these DMUs. However, a deep insight into clarifying the power’s differences between the internal structures of DMUs is a deficiency in the current UNDEA model. To address this issue, in this paper, we propose a new UNDEA model by differentiating the power asymmetry of each sub-stage with assumption of a two-stage system and demonstrate an additive relationship between stage 1 and stage 2 of each DMU. Moreover, the equivalent form and its proof of the new model are also presented for accurate calculation. Finally, a numerical example reflecting three different additive relationships between two sub-stages of DMUs is given to illustrate the results of evaluation.

Decision support systems (DSS) are currently developing rapidly and are increasingly used in various fields. More often, those systems are inseparable from information-based systems and computer systems. Therefore, from a methodical point of view, the algorithms implemented in the DSS play a critical role. In this aspect, multi-criteria decision support (MCDA) methods are widely used. As research progresses, many MCDA methods and algorithms for the objective identification of the significance of individual criteria of the MCDA models were developed. In this paper, an analysis of available objective methods for criteria weighting is presented. Additionally, the authors presented the implementation of the system that provides easy and accessible weight calculations for any decision matrix with the possibility of comparing results of different weighting methods. The results of weighting methods were compared using carefully selected similarity coefficients to emphasise the correlation of the resulting weights. The performed research shows that every method should provide distinctive weights considering input data, emphasising the importance of choosing the correct method for a given multi-criteria decision support model and DSS.

Blind image deblurring is a well-known ill-posed inverse problem in the computer vision field. To make the problem well-posed, this paper puts forward a plain but effective regularization method, namely spectral norm regularization (SN), which can be regarded as the symmetrical form of the spectral norm. This work is inspired by the observation that the SN value increases after the image is blurred. Based on this observation, a blind deblurring algorithm (BDA-SN) is designed. BDA-SN builds a deblurring estimator for the image degradation process by investigating the inherent properties of SN and an image gradient. Compared with previous image regularization methods, SN shows more vital abilities to differentiate clear and degraded images. Therefore, the SN of an image can effectively help image deblurring in various scenes, such as text, face, natural, and saturated images. Qualitative and quantitative experimental evaluations demonstrate that BDA-SN can achieve favorable performances on actual and simulated images, with the average PSNR reaching 31.41, especially on the benchmark dataset of Levin et al.

This paper investigates the symmetry breaking between the polarizations of Λ and Λ¯ hyperons in relativistic collisions of heavy ions at intermediate and low energies. The microscopic transport model UrQMD is employed to study the thermal vorticity of hot and dense nuclear matter formed in non-central Au + Au collisions at center-of-mass energies 7.7≤sNN≤62.4 GeV. The whole volume of an expanding fireball is subdivided into small cubic cells. Then, we trace the final Λ and Λ¯ hyperons back to their last interaction point within a certain cell. Extracting the bulk parameters, such as energy density, net baryon density, and net strangeness of the hot and dense medium in the cell, one can obtain the cell temperature and the chemical potentials at the time of the hyperon emission. To do this, the extracted characteristics have to be fitted to the statistical model (SM) of ideal hadron gas. After that, the vorticity of nuclear matter and polarization of both hyperons are calculated. We found that the polarization of both Λ and Λ¯ increases with decreasing energy of heavy-ion collisions. The stronger polarization of Λ¯ is explained by (i) the slightly different freeze-out conditions of both hyperons and (ii) the different space–time distributions of Λ and Λ¯.

The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals of the Peetre-type. In a distinct section we indicate a generalization of these operators that is useful in approximating vector functions with real values defined on the hypercube [0,1]q, q&gt, 1. The study involves achieving a parallelism between different classes of linear and positive operators, which will highlight a symmetry between these approximation processes.

In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which in turn open up opportunities to easily find their solutions. In this paper, we study the symmetry between differential geometry of surfaces/curves and some integrable generalized spin systems. In particular, we investigate the gauge and geometrical equivalence between the local/nonlocal nonlinear Schrödinger type equations (NLSE) and the extended continuous Heisenberg ferromagnet equation (HFE) to investigate how nonlocality properties of one system are inherited by the other. First, we consider the space curves induced by the nonlinear Schrödinger-type equations and its equivalent spin systems. Such space curves are governed by the Serret–Frenet equation (SFE) for three basis vectors. We also show that the equation for the third of the basis vectors coincides with the well-known integrable HFE and its generalization. Two other equations for the remaining two vectors give new integrable spin systems. Finally, we investigated the relation between the differential geometry of surfaces and integrable spin systems for the three basis vectors.

In order to adapt to the rapid development of network technology and network security detection in different scenarios, the generalization ability of the classifier needs to be further improved and has the ability to detect unknown attacks. However, the generalization ability of a single classifier is limited to dealing with class imbalance, and the previous ensemble methods inevitably increase the training cost. Therefore, in this paper, a novel network intrusion detection algorithm combined with group convolution is proposed to improve the generalization performance of the model. The basic classifier uses group convolution with symmetric structure instead of ordinary convolution neural network, which is trained by the cyclic cosine annealing learning rate. Through snapshot ensemble, the generalization ability of the integration model is improved without increasing the training cost. The effectiveness of this method is proved on NSL-KDD and UNSW-NB15 datasets compared to six other ensemble methods, the classification accuracy can achieve 85.82% and 80.38%, respectively.

Automated mechanical transmission (AMT) is used as a soft starter in this paper. To improve the soft starting quality, a novel data-driven method is studied. By analyzing and comparing five common soft-starting acceleration curves, a segmented acceleration curve is put forward to be used as the soft-starting acceleration curve for the AMT. Based on the prototype model free adaptive control (MFAC) method, a modified MFAC method with jerk compensation is given to control the AMT output shaft’s angular acceleration and reduce driveline shock. Compared with the methods of prototype MFAC and traditional proportion integration differentiation (PID), the modified MFAC method with jerk compensation can better control the AMT output shaft’s angular acceleration and has excellent characteristics in terms of small tracking error and smaller shock. The research results provide a novel data-driven method for AMT as a soft starter.

A proper total k-coloring ϕ of G with ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each uv∈E(G) is called a total neighbor sum distinguishing k-coloring, where EG(u)={uv|uv∈E(G)}. Pilśniak and Woźniak conjectured that every graph with maximum degree Δ exists a total neighbor sum distinguishing (Δ+3)-coloring. In this paper, we proved that any IC-planar graph with Δ≥12 satisfies this conjecture, which improves the result of Song and Xu.

To process high-frequency signals on a printed circuit board (PCB), it is often necessary to carefully analyze and select the pad widths of the chip packages and components to match their impedance to the standard Z0. Modern PCBs are complex multilayer designs, utilizing either only high-end laminates, low-end laminates, or a combination of both. The on-board component footprints usually have larger pads that become discontinuities and corrupt the impedance of critical traces. One way to address this issue is to include reference plane cutouts as a measure of compensation. This paper aims to find out how an asymmetric dielectric stack-up affects the microstrip discontinuity impedance compensation using reference plane cutouts. The selected board layer stack-up imitates several different practical design scenarios, including costly PCBs that strictly comprise high-end dielectric materials, as well as trying to lower PCB cost by introducing low-cost materials without major performance sacrifice. S-parameter measurements are performed and confirmed by time domain reflectometry (TDR) measurements.

Several interesting physical phenomena and industrial applications explained by the dressed photon have been reported in recent years. These require a novel concept in an off-shell science that deviates from the conventional optics, satisfying energy and momentum conservation laws. In this paper, starting from an original model that captures dressed-photon characteristics phenomenologically, the dynamics of the dressed photon in a nanomatter system and the mechanism for extracting internal degrees of freedom of the dressed photon to an external space have been examined by theoretical and numerical approaches. Our proposal is that basis states of the dressed photon can be transformed to the form that reflects the spatial distribution of the dressed-photon steady state in the system, and some of basis states with predetermined spatial distribution can relate to the dissipation components in the external space by means of the renormalization technique. From the results of numerical simulation, it is found that quasi-static states are regarded as the photon with light mass or massless, and the extraction of active states strongly affects the spatial distribution in a new steady state. The concept for extracting dressed-photon energy to an external space will contribute to a detailed understanding of dressed-photon physics and future industrial applications.

In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In particular, the single peakon, two-peakon, stationary kink, anti-kink, two-kink, two-anti-kink, bell-shape soliton and hat-shape soliton solutions are presented in an explicit formula.

Orthodontic treatment carries the risk of major complications such as enamel demineralization, tooth decay, gingivitis, and periodontal damage. A large number of elements of fixed orthodontic appliance results in the creation of additional plaque retention sites which increase the risk of biofilm creation. Modification of the surface of orthodontic elements may prevent the formation of bacterial biofilm. In this paper, surface modification of stainless steel orthodontic wires with TiO2: Ag was carried out by the sol-gel thin film dip-coating method. To obtain the anatase crystal structure, substrates were calcined for 2 h at 500 °C. The properties of the obtained coatings were investigated using scanning electron microscopy, X-ray diffraction, and electrochemical tests. Corrosion studies were performed in a Ringer’s solution, which simulated physiological solution. SEM and XRD analyses of the coated surface confirmed the presence of Ag nanoparticles which may have antimicrobial potential.

Although hyperspectral data provide rich feature information and are widely used in other fields, the data are still scarce. Training small sample data classification is still a major challenge for HSI classification based on deep learning. Recently, the method of mining sample relationships has been proved to be an effective method for training small samples. However, this strategy requires high computational power, which will increase the difficulty of network model training. This paper proposes a modified depthwise separable relational network to deeply capture the similarity between samples. In addition, in order to effectively mine the similarity between samples, the feature vectors of support samples and query samples are symmetrically spliced. According to the metric distance between symmetrical structures, the dependence of the model on samples can be effectively reduced. Firstly, in order to improve the training efficiency of the model, depthwise separable convolution is introduced to reduce the computational cost of the model. Secondly, the Leaky-ReLU function effectively activates all neurons in each layer of neural network to improve the training efficiency of the model. Finally, the cosine annealing learning rate adjustment strategy is introduced to avoid the model falling into the local optimal solution and enhance the robustness of the model. The experimental results on two widely used hyperspectral remote sensing image data sets (Pavia University and Kennedy Space Center) show that compared with seven other advanced classification methods, the proposed method achieves better classification accuracy under the condition of limited training samples.

Carbon fiber-reinforced polymer (CFRP) reinforcement technology has been widely used in the reinforcement of reinforced concrete (RC) beams. At this stage, high prestressed CFRP board reinforcement is often used in actual reinforcement. However, most reinforced bridges are designed for a long time, and the design value of the protective layer is low, and it is impossible to achieve a large prestressed tension. Therefore, this paper proposes the reverse-arch method to paste the CFRP board and apply low prestress to strengthen the symmetrical RC beam. Through the three-point forward loading test, the cracking load, ultimate load, crack width, mid-span deflection, strain and failure mode of a reverse-arch method-pasted CFRP board-reinforced beam, a directly pasted CFRP board-reinforced beam and an unreinforced beam are compared. The results show that the load-bearing capacity and stiffness of the test beam can be improved by pasting CFRP plates with anti-arch method, but the ductility of the test beam is reduced. Compared with the unreinforced beam, the maximum cracking load and ultimate load are increased by 56% and 63% respectively. The reverse-arch method can produce low prestress, improve the stiffness and bearing capacity of members, and has a good prospect of engineering application.