Search

With the rapid development of information technology, the transmission of information has become convenient. In order to prevent the leakage of information, information security should be valued. Therefore, the data hiding technique has become a popular solution. The reversible data hiding technique (RDH) in particular uses symmetric encoding and decoding algorithms to embed the data into the cover carrier. Not only can the secret data be transmitted without being detected and retrieved completely, but the cover carrier also can be recovered without distortion. Moreover, the encryption technique can protect the carrier and the hidden data. However, the encrypted carrier is a form of ciphertext, which has a strong probability to attract the attention of potential attackers. Thus, this paper uses the generative adversarial networks (GAN) to generate meaningful encrypted images for RDH. A four-stage network architecture is designed for the experiment, including the hiding network, the encryption/decryption network, the extractor, and the recovery network. In the hiding network, the secret data are embedded into the cover image through residual learning. In the encryption/decryption network, the cover image is encrypted into a meaningful image, called the marked image, through GMEI-GAN, and then the marked image is restored to the decrypted image via the same architecture. In the extractor, 100% of the secret data are extracted through the residual learning framework, same as the hiding network. Lastly, in the recovery network, the cover image is reconstructed with the decrypted image and the retrieved secret data through the convolutional neural network. The experimental results show that using the PSNR/SSIM as the criteria, the stego image reaches 45.09 dB/0.9936 and the marked image achieves 38.57 dB/0.9654. The proposed method not only increases the embedding capacity but also maintains high image quality in the stego images and marked images.

This paper considers the Modified Autonomous Van der Pol–Duffing equation subjected to dynamic state feedback, which can well characterize the dynamic behaviors of the nonlinear dynamical systems. Both the issues of local stability switches and the Hopf bifurcation versus time delay are investigated. Associating with the τ decomposition strategy and the center manifold theory, the delay stable intervals and the direction and stability of the Hopf bifurcation are all determined. Specifically, the computation of purely imaginary roots (symmetry to the real axis), the positive real root formula for cubic equation and the sophisticated bilinear form of adjoint operators are proposed, which make the calculations mentioned in our discussion unified and simple. Finally, the typical numerical examples are shown to illustrate the correctness and effectiveness of the practical technique.

Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods. In this article, an Ostrowski-type method for solving equations in Banach space is extended. This is achieved by finding a stricter set than before containing the iterates. The convergence analysis becomes finer. Due to the general nature of our technique, it can be utilized to enlarge the utilization of other methods. Examples finish the paper.

Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third Bessel functions, we derive necessary and sufficient conditions for which the new generalized operators belong to the class of q-starlike functions of order alpha. Several corollaries and consequences of the main results are also pointed out.

This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

This paper is devoted to studying approximations of symmetric continuous functions by symmetric analytic functions on a Banach space X with a symmetric basis. We obtain some positive results for the case when X admits a separating polynomial using a symmetrization operator. However, even in this case, there is a counter-example because the symmetrization operator is well defined only on a narrow, proper subspace of the space of analytic functions on X. For X=c0, we introduce ε-slice G-analytic functions that have a behavior similar to G-analytic functions at points x∈c0 such that all coordinates of x are greater than ε, and we prove a theorem on approximations of uniformly continuous functions on c0 by ε-slice G-analytic functions.

Unmanned aerial vehicle (UAV) clusters usually face problems such as complex environments, heterogeneous combat subjects, and realistic interference factors in the course of mission assignment. In order to reduce resource consumption and improve the task execution rate, it is very important to develop a reasonable allocation plan for the tasks. Therefore, this paper constructs a heterogeneous UAV multitask assignment model based on several realistic constraints and proposes an improved half-random Q-learning (HR Q-learning) algorithm. The algorithm is based on the Q-learning algorithm under reinforcement learning, and by changing the way the Q-learning algorithm selects the next action in the process of random exploration, the probability of obtaining an invalid action in the random case is reduced, and the exploration efficiency is improved, thus increasing the possibility of obtaining a better assignment scheme, this also ensures symmetry and synergy in the distribution process of the drones. Simulation experiments show that compared with Q-learning algorithm and other heuristic algorithms, HR Q-learning algorithm can improve the performance of task execution, including the ability to improve the rationality of task assignment, increasing the value of gains by 12.12%, this is equivalent to an average of one drone per mission saved, and higher success rate of task execution. This improvement provides a meaningful attempt for UAV task assignment.

In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa’s approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.

Over recent years, the incidence of data breaches and cyberattacks has increased significantly. This has highlighted the need for sectoral organizations to share information about such events so that lessons can be learned to mitigate the prevalence and severity of cyber incidents against other organizations. Sectoral organizations embody a governance relationship between cross-sector public and private entities, called public-private partnerships (PPPs). However, organizations are hesitant to share such information due to a lack of trust and business-critical confidentially issues. This problem occurs because of the absence of any protocols that guarantee privacy protection and protect sensitive information. To address this issue, this paper proposes a novel protocol, Putra-Ramli Secure Cyber-incident Information Sharing (PURA-SCIS), to secure cyber incident information sharing. PURA-SCIS has been designed to offer exceptional data and privacy protection and run on the cloud services of sectoral organizations. The relationship between organizations in PURA-SCIS is symmetrical, where the entities must collectively maintain the security of classified cyber incident information. Furthermore, the organizations must be legitimate entities in the PURA-SCIS protocol. The Scyther tool was used for protocol verification in PURA-SCIS. The experimental results showed that the proposed PURA-SCIS protocol provided good security properties, including public verifiability for all entities, blockless verification, data privacy preservation, identity privacy preservation and traceability, and private information sharing. PURA-SCIS also provided a high degree of confidentiality to protect the security and integrity of cyber-incident-related information exchanged among sectoral organizations via cloud services.

The electricity distribution system is the coupling point between the utility and the end-user. Typically, these systems have unbalanced feeders due to the variety of customers’ behaviors. Some significant problems occur, the unbalanced loads increase the operational cost and system investment. In radial distribution systems, swapping loads between the three phases is the most effective method for phase balancing. It is performed manually and subjected to load flow equations, capacity, and voltage constraints. Recently, due to smart grids and automated networks, dynamic phase balancing received more attention, thus swapping the loads between the three phases automatically when unbalance exceeds permissible limits by using a remote-controlled phase switch selector/controller. Automatic feeder reconfiguration and phase balancing eliminates the service interruption, enhances energy restoration, and minimize losses. In this paper, a case study from the Irbid district electricity company (IDECO) is presented. Optimal reconfiguration of phase balancing using three techniques: feed-forward back-propagation neural network (FFBPNN), radial basis function neural network (RBFNN), and a hybrid are proposed to control the switching sequence for each connected load. The comparison shows that the hybrid technique yields the best performance. This work is simulated using MATLAB and C programming language.

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

Symmetry (and group theory) is a fundamental principle of theoretical physics. Finite symmetries, continuous symmetries of compact groups, and infinite-dimensional representations of noncompact Lie groups are at the core of solid physics, particle physics, and quantum physics, respectively. The latter groups now play an important role in many branches of mathematics. In more recent years, we have been faced with the impact of topological quantum field theory (TQFT). Topology and symmetry have deep connections, but topology is inherently broader and more complex. While the presence of symmetry in physical phenomena imposes strong constraints, topology seems to be related to low-energy states and is very likely to provide information about the different dynamical trajectories and patterns that particles can follow. For example, regarding the relationship of topology to low-energy states, Hodge’s theory of harmonic forms shows that the zero-energy states (for differential forms) correspond to the cohomology. Regarding the relationship of topology to particle trajectories, a topological knot can be seen as an orbit with complex properties in spacetime. The various deformations or embeddings of the knot, performed in low or high dimensions, allow defining different equivalence classes or topological types, and interestingly, it is possible from these types to study the symmetries associated with the deformations and their changes. More specifically, in the present work, we address two issues: first, that quantum geometry deforms classical geometry, and that this topological deformation may produce physical effects that are specific to the quantum physics scale, and second, that mirror symmetry and the phenomenon of topological change are closely related. This paper was aimed at understanding the conceptual and physical significance of this connection.

In engineering application, the hot press assembly technology is often used to improve the stability of the rotor structure, but the conventional design methods cannot effectively evaluate the influence of this process on the rotor strength, which easily causes the rotor strength to exceed its safety margin range, and seriously it will lead to the failure of the rotor structure. This paper takes the cylindrical magnet surface-mounted high-speed permanent magnet synchronous motor rotor as the research object. Firstly, the influence of the assembly pressing force on the rotor stresses and interference is analyzed; then, comprehensively considering the assembly pressing force, speed and temperature, the rotor strength’s design method with high structural stability is proposed. Finally, based on the proposed method, the rotor strength of a 100 kW/30,000 rpm high-speed motor is designed, and the feasibility of the design is verified by over-speed experiment.

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

Railway infrastructures have played a critical role to ensure the continuity of goods and passenger transportation in China. Under extreme loading and environmental conditions, railway structures are vulnerable to deterioration and failure, leading to the interruption of the whole transportation system. Several techniques have been used for the health monitoring of railway structures. Optical fiber sensors are the widely recognized technique due to their inherent advantages such as high sensitivity, anti-electromagnetic interference, light weight, tiny size, corrosion resistance, and easy integration and network configuration. This paper provides a state-of-the-art of optical fiber sensing technologies and their practical application in railway infrastructures. In addition, the strain transfer analysis of optical fiber sensors is described for parameter reflection. A smart concept for artificial intelligence contribution is also declared. Finally, existing and future prospects on smart concept-based optical fiber sensors for railway infrastructure are discussed. The study can provide useful guidance to understand the problems in artificial intelligence which contributed to the Structural Health Monitoring system of railway structures.

In 2002, Agrawal and Kiernan defined six basic requirements, including preventing illegal watermark embedding and authentication, reversibility, robustness, and others, which must be satisfied when a reversible watermark is designed for relational databases. To meet these requirements, in this paper, a lossless watermarking scheme for a categorical relational database called LRW-CRDB (lossless robust watermarking for categorical relational databases) is proposed. In our LRW-CRDB scheme, the database owner needs to generate two secret embedding keys, K1 and K2, in advance. Then, two reference sets are generated based on two different secret embedding keys and a symmetry-based data hiding strategy, and then these are used for the watermark embedding phases. Experimental results confirmed that our LRW-CRDB scheme successfully detects 100% of hidden watermarks, even when more than 95% of the watermarked relational database has been deleted. In other words, the robustness of our proposed LRW-CRDB scheme outperforms other existing schemes under a variety of possible attacks, such as alteration, sorting, deletion, and mix-match attacks.

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.

This paper highlights algebraic and mathematical properties in symmetry with Petri nets in order to control automated systems such as flexible workshops, which represent one of the most important examples in industry and for discrete event systems in general. This project deals with the problem of forbidden state transition by using a new application of the theory of regions for supervisory control. In the literature, most control synthesis methods suffer greatly from a cumbersome calculation burden of the Petri net supervisor given the complex exploration of the state graph. Our new methodology lightens the computational load of the Petri net supervisor by choosing specific regions on the reachability graph, on which the control is calculated offline using CPLEX. The determined controller is activated online if the process enters the chosen region, and deactivated otherwise. All our experiments were applied in a flexible workshop implemented in our research laboratory, which was used to engrave selected models on glass blocks of different colors.

Path planning plays an essential role in mobile robot navigation, and the A* algorithm is one of the best-known path planning algorithms. However, the conventional A* algorithm and the subsequent improved algorithms still have some limitations in terms of robustness and efficiency. These limitations include slow algorithm efficiency, weak robustness, and collisions when robots are traversing. In this paper, we propose an improved A*-based algorithm called EBHSA* algorithm. The EBHSA* algorithm introduces the expansion distance, bidirectional search, heuristic function optimization and smoothing into path planning. The expansion distance extends a certain distance from obstacles to improve path robustness by avoiding collisions. Bidirectional search is a strategy that searches for a path from the start node and from the goal node at the same time. Heuristic function optimization designs a new heuristic function to replace the traditional heuristic function. Smoothing improves path robustness by reducing the number of right-angle turns. Moreover, we carry out simulation tests with the EBHSA* algorithm, and the test results show that the EBHSA* algorithm has excellent performance in terms of robustness and efficiency. In addition, we transplant the EBHSA* algorithm to a robot to verify its effectiveness in the real world.

The early diagnosis of retinopathy is crucial to the prevention and treatment of diabetic retinopathy. The low proportion of positive cases in the asymmetric microaneurysm detection problem causes preprocessing to treat microaneurysms as noise to be eliminated. To obtain a binary image containing microaneurysms, the object was segmented by a symmetry algorithm, which is a combination of the connected components and SSA methods. Next, a candidate microaneurysm set was extracted by multifeature clustering of binary images. Finally, the candidate microaneurysms were mapped to the Radon frequency domain to achieve microaneurysm detection. In order to verify the feasibility of the algorithm, a comparative experiment was conducted on the combination of the connected components and SSA methods. In addition, PSNR, FSIM, SSIM, fitness value, average CPU time and other indicators were used as evaluation standards. The results showed that the overall performance of the binary image obtained by the algorithm was the best. Last but not least, the accuracy of the detection method for microaneurysms in this paper reached up to 93.24%, which was better than that of several classic microaneurysm detection methods in the same period.

Making use of a post-quantum derivative operator, we define two classes of meromorphic analytic functions. For the considered family of functions, we aim to investigate the sharp bounds’ values in the case of the Fekete–Szegö problem. The study of the well-known Fekete–Szegö functional in the post-quantum calculus case for meromorphic functions provides new outcomes for research in the field. With the extended p,q-operator, we establish certain inequalities’ relations concerning meromorphic functions. In the final part of the paper, a new p,q-analogue of the q-Wright type hypergeometric function is introduced. This function generalizes the classical and symmetrical Gauss hypergeometric function. All the obtained results are sharp.

In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.

When working with Markov chains, especially if they are of order greater than one, it is often necessary to evaluate the respective contribution of each lag of the variable under study on the present. This is particularly true when using the Mixture Transition Distribution model to approximate the true fully parameterized Markov chain. Even if it is possible to evaluate each transition matrix using a standard association measure, these measures do not allow taking into account all the available information. Therefore, in this paper, we introduce a new class of so-called "predictive power" measures for transition matrices. These measures address the shortcomings of traditional association measures, so as to allow better estimation of high-order models.

To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for $so(2p+1)_2$. These categories describe non-abelian anyons dubbed `metaplectic anyons'. We obtain explicit expressions for all the $F$- and $R$-symbols. Based on these, we conjecture a classification for their monoidal equivalence classes from an analysis of their gauge invariants and define a function which gives us the number of classes., 28 pages; v2: minor changes

Symmetry-based channel digital twin is a great technology which can reproduce the communication channel of real scenes for performance evaluation of the wireless sensor network (WSN) inside tower buildings, based on the ray tracing (RT) method and machine learning (ML) theories, a cluster-based channel model is proposed in this paper. Meanwhile, an improved k-means method, which considers the weight of different dimensions in the multipath component distance (MCD) is presented for clustering, which has better clustering performance over the sparsity-based algorithm and traditional k-means algorithm. Moreover, the channel parameters such as cluster delay and cluster power are also investigated. On this basis, the communication performance of WSN, i.e., bit error rate (BER) and channel capacity are derived and analyzed. The simulation and analysis results show that the cluster model based on the RT method can get approximately equivalent channel impulse response (CIR), and the BER of proposed model is consistent with the simulated one. These results can provide reference for the node layout and optimization of WSN inside tower buildings.

In this paper, we present a variety of existence theorems for maximal type elements in a general setting. We consider multivalued maps with continuous selections and multivalued maps which are admissible with respect to Gorniewicz and our existence theory is based on the author’s old and new coincidence theory. Particularly, for the second section we present presents a collectively coincidence coercive type result for different classes of maps. In the third section we consider considers majorized maps and presents a variety of new maximal element type results. Coincidence theory is motivated from real-world physical models where symmetry and asymmetry play a major role.

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in Cn, hyperconvex bounded domains, and so on.

An antimagic labeling of a graph G is a bijection f:E(G)→{1,…,|E(G)|} such that the weights w(x)=∑y∼xf(y) distinguish all vertices. A well-known conjecture of Hartsfield and Ringel (1990) is that every connected graph other than K2 admits an antimagic labeling. For a set of distances D, a D-antimagic labeling of a graph G is a bijection f:V(G)→{1,…,|V(G)|} such that the weightω(x)=∑y∈ND(x)f(y) is distinct for each vertex x, where ND(x)={y∈V(G)|d(x,y)∈D} is the D-neigbourhood set of a vertex x. If ND(x)=r, for every vertex x in G, a graph G is said to be (D,r)-regular. In this paper, we conjecture that a graph admits a D-antimagic labeling if and only if it does not contain two vertices having the same D-neighborhood set. We also provide evidence that the conjecture is true. We present computational results that, for D={1}, all graphs of order up to 8 concur with the conjecture. We prove that the set of (D,r)-regular D-antimagic graphs is closed under union. We provide examples of disjoint union of symmetric (D,r)-regular that are D-antimagic and examples of disjoint union of non-symmetric non-(D,r)-regular graphs that are D-antimagic. Furthermore, lastly, we show that it is possible to obtain a D-antimagic graph from a previously known distance antimagic graph.

In this paper, a method for detecting real-time images that include counterlight produced by the sun, is proposed. It involves applying a multistep analysis of the size, location, and distribution of bright areas in the image. In general, images containing counterlight have a symmetrically high brightness value at a specific location spread over an extremely large region. In addition, the distribution and change in brightness in that specific region have a symmetrically large difference compared with other regions. Through a multistep analysis of these symmetrical features, it is determined whether counterlight is included in the image. The proposed method presents a processing time of approximately 0.7 s and a detection accuracy of 88%, suggesting that the approach can be applied to a safe driving support system for autonomous vehicles.

This paper is devoted to the problem of prescribed performance trajectory tracking control for symmetrical underactuated unmanned surface vessels (USVs) in the presence of model uncertainties and input quantization. By combining backstepping filter mechanisms and adaptive algorithms, two robust control architectures are investigated for surge motion and yaw motion. To guarantee the prespecified performance requirements for position tracking control, the constrained error dynamics are transformed to unconstrained ones by virtue of a tangent-type nonlinear mapping function. On the other hand, the inaccurate model can be identified through radial basis neural networks (RBFNNs), where the minimum learning parameter (MLP) algorithm is employed with a low computational complexity. Furthermore, quantization errors can be effectively reduced even when the parameters of the quantizer remain unavailable to designers. Finally, the effectiveness of the proposed controllers is verified via theoretical analyses and numerical simulations.

The results of this paper allow one to derive several results of general interest: to prove the Schiffer’s conjecture, to solve the Pompeiu problem, to prove two symmetry results in harmonic analysis and to give a new method for solving an old symmetry problem.

In this paper, we propose a CPG (central pattern generator) network control system using motor dynamics for the gait planning of a quadruped robot with a trot walking pattern to climb up and down a slope and turn back and follow the symmetry of route. The CPG unit model, which includes two DC motors model, has the ability to generate the periodic joint angle with complex-value parameters. Through plural feedback parameters, the CPG network can adjust the frequency and amplitude of an internal neuron model such as a robot meeting an irregular surface of a road. Using the stride length and frequency of robot joint angles, the distance of walking with a trot pattern can be calculated. In order to confirm the validity of the proposed control system, a quadruped robot is produced to implement the adaptive walking system.

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and describe the norms induced by such inner products. Among other results, Hilbert groups, midconvex and orthogonal subgroups are presented, and a Riesz representation theorem on divisible Hilbert groups is proved.

In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt–Poincaré method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt–Poincaré method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions.

X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain data-driven tight frame regularization, the proposed NLR-DDTF model uses an asymmetric treatment for image reconstruction and Radon domain inpainting, which combines the nonlocal low-rank approximation method for spatial domain CT image reconstruction and data-driven tight frame-based regularization for Radon domain image inpainting. An alternative direction minimization algorithm is designed to solve the proposed model. Several numerical experiments and comparisons are provided to illustrate the superior performance of the NLR-DDTF method.

The energy manufacturers are required to produce an accurate amount of energy by meeting the energy requirements at the end-user side. Consequently, energy prediction becomes an essential role in the electric industrial zone. In this paper, we propose the hybrid ensemble deep learning model, which combines multilayer perceptron (MLP), convolutional neural network (CNN), long short-term memory (LSTM), and hybrid CNN-LSTM to improve the forecasting performance. These DL architectures are more popular and better than other machine learning (ML) models for time series electrical load prediction. Therefore, hourly-based energy data are collected from Jeju Island, South Korea, and applied for forecasting. We considered external features associated with meteorological conditions affecting energy. Two-year training and one-year testing data are preprocessed and arranged to reform the times series, which are then trained in each DL model. The forecasting results of the proposed ensemble model are evaluated by using mean square error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Error metrics are compared with DL stand-alone models such as MLP, CNN, LSTM, and CNN-LSTM. Our ensemble model provides better performance than other forecasting models, providing minimum MAPE at 0.75%, and was proven to be inherently symmetric for forecasting time-series energy and demand data, which is of utmost concern to the power system sector.

The object of this paper is to derive a double integral in terms of the Hurwitz–Lerch zeta function. Almost all Hurwitz–Lerch zeta functions have an asymmetrical zero-distribution. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.

The information technique has developed rapidly. The technique of QR codes is widely applied in our daily life, and the mechanism is suitable to share data. A QR code uses symmetric encryption to store and retrieve data efficiently. However, the security issues of QR codes are seldom discussed by the wider community. Moreover, if the sender wishes only the authorized participant to attain the private data which are shared, the data must be encrypted. Furthermore, we do not know who should be censured when problems arise. In view of this, to maintain the integrity and the confidentiality of information security, this paper proposed a new puzzle-based data sharing scheme to share the private information safely. Firstly, we generated the digital signature of the information, then applied the random grids algorithm to obtain the shares. Then, we disarrayed the shares which contain the information and the digital signature with a puzzle-based encoding method. Afterwards, we concealed them into the cover QR codes. With the QR code mechanism of error correction, the marked QR code remain meaningful. Finally, we could send marked QR codes via transmission. The receiver could use XOR operation to obtain the private information after solving the puzzles and verify whether it was tampered with by the digital signature. The proposed system can recover the lossless data and protect them from being divulged. To deal with the potential hazard of transmission in a public environment, there are more and more studies on data hiding and image authentication.

An uncertain random variable is a tool used to research indeterminacy quantities involving randomness and uncertainty. The concepts of an ’uncertain random process’ and an ’uncertain random renewal process’ have been proposed in order to model the evolution of an uncertain random phenomena. This paper designs a new uncertain random process, called the uncertain random delayed renewal process. It is a special type of uncertain random renewal process, in which the first arrival interval is different from the subsequent arrival interval. We discuss the chance distribution of the uncertain random delayed renewal process. Furthermore, an uncertain random delay renewal theorem is derived, and the chance distribution limit of long-term expected renewal rate of the uncertain random delay renewal system is proved. Then its average uncertain random delay renewal rate is obtained, and it is proved that it is convergent in the chance distribution. Finally, we provide several examples to illustrate the consistency with the existing conclusions.

In this paper, we present an iterative method based on the well-known Ulm’s method to numerically solve Fredholm integral equations of the second kind. We support our strategy in the symmetry between two well-known problems in Numerical Analysis: the solution of linear integral equations and the approximation of inverse operators. In this way, we obtain a two-folded algorithm that allows us to approximate, with quadratic order of convergence, the solution of the integral equation as well as the inverses at the solution of the derivative of the operator related to the problem. We have studied the semilocal convergence of the method and we have obtained the expression of the method in a particular case, given by some adequate initial choices. The theoretical results are illustrated with two applications to integral equations, given by symmetric non-separable kernels.

In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models.

The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by solving a Ermakov-Milne-Pinney equation. Their mapping ``Eisenhart-Duval'' lifts as a conformal transformation between two appropriate Bargmann spaces. The quantum propagator is calculated also by bringing the quadratic system to free form by another time-dependent Bargmann-conformal transformation which generalizes the one introduced before by Niederer and is related to the mapping proposed by Arnold. Our approach allows us to extend the Maslov phase correction to arbitrary time-dependent frequency. The method is illustrated by the Mathieu profile., Comment: This paper celebrates the 90th birthday of Akira Inomata. 28 pages, 5 figures. Matches published version