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In this paper we provide a new parametrization of the characteristic curve (I - V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I - V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I - V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I - V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I - V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster. • A parametrization of the photovoltaic single-diode model. • Calculus of the Euclidean distance (ED) to an I - V curve. • The point of maximum curvature and the evolute of an I - V curve. • Fast and fail-safe algorithm to compute the ED to an I - V curve. • The ED algorithm to perform a robust orthogonal distance regression. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework. [Copyright &y& Elsevier]

Abstract: In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified. [Copyright &y& Elsevier]

This paper aims to study an HIV model with age structure and latently in a spatially homogeneous environment. By applying the fixed point theorem, we obtain the existence of the global solution and the global attractor for the model. We also identify the explicit formula of the basic reproduction number by the mean of the Laplace transformation, and confirm that this number predicts whether the infection occurs or not. Through analyzing the root distribution of the characteristic equation, the local stability of the equilibrium is obtained. By appealing to the appropriate Lyapunov functionals, we further study the global stability of the equilibrium. Numerical simulations also validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an epidemic model with homogeneous Dirichlet boundary condition is formulated to study the joint impact of spatial diffusion, infection age and treatment adherence on the HIV/AIDS transmission among humans. It is an interesting problem to understand the threshold dynamics of HIV/AIDS model with the above three factors. Since the complexity of the model and specificity of the boundary condition, there are two main mathematical challenges: i). the compactness of the solution map is not guaranteed; ii). the explicit expression of the basic reproduction cannot be given even if the parameters are spatially independent. We first discuss the well-posedness of the system, then we identify the basic reproduction number R 0 as the spectral radius of the next generation operator, followed by the global attractivity of disease-free steady state when R 0 < 1 , the uniform persistence of the disease and the existence of the endemic steady state when R 0 > 1. Numerical simulations are carried out to illustrate our theoretical results, which suggest that the diffusion of individuals has an opposite effect on the disease outbreaks, and improving the treatment compliance of HIV infected individuals can control HIV transmission among the population effectively. [ABSTRACT FROM AUTHOR]

• It is observed that regular convergence indicators are more focused on the convergence and may neglect the extent of the spread. • This paper designs an adaptive reference vector strategy, which is able to take into account the convergence and the extent of the spread, simultaneously. • A new algorithm is proposed and tested on multiple test suites.. Convergence is always a major concern for many-objective optimization problems. Over the past few decades, various methods have been designed for measuring the convergence. However, according to our mathematical and empirical analyses, most of these methods are more focused on the convergence, and may neglect the exploration of boundary solutions, resulting in the incomplete Pareto fronts and the poor extent of spread achieved among the obtained non-dominated solutions. Regarding this issue, this paper proposes a Many-Objective Evolutionary Algorithm with Adaptive Reference Vector (MaOEA-ARV). In MaOEA-ARV, an adaptive reference vector strategy is designed to dynamically adjust the reference vectors according to the current distribution of candidate solutions for ensuring the spread and convergence simultaneously. Additionally, a hierarchical clustering strategy is employed to adaptively partition candidate solutions into multiple clusters for the diversity of candidate solutions. Experimental results on DTLZ, BT, ZDT and WFG test suites with up to 12 objectives demonstrate the effectiveness of MaOEA-ARV. [ABSTRACT FROM AUTHOR]

Stefan melting problems involve the tracking of a sharp melt front during the heat conduction controlled melting of a solid. A feature of this problem is a jump discontinuity in the heat flux across the melt interface. Time fractional versions of this problem introduce fractional time derivatives into the governing equations. Starting from an appropriate thermodynamic balance statement, this paper develops a new sharp interface time fractional Stefan melting problem, the memory-enthalpy formulation. A mathematical analysis reveals that this formulation exhibits a natural regularization in that, unlike the classic Stefan problem, the flux is continuous across the melt interface. It is also shown how the memory-enthalpy formulation, along with previously reported time fractional Stefan problems based on a memory-flux, can be derived by starting from a generic continuity equation and melt front condition. The paper closes by mathematically proving that the memory-enthalpy fractional Stefan formulation is equivalent to the previous memory-flux formulations. A result that provides a thermodynamic consistent basis for a widely used and investigated class of time fractional (memory) Stefan problems. • A new time fractional Stefan problem is presented, the memory-enthalpy formulation. • The problem is obtained from an appropriate thermodynamic balance statement. • We prove that this formulation exhibits a natural regularization of the problem. • A comparison with the previous memory-flux formulation is made. • We prove that the memory-enthalpy formulation is equivalent to the memory-flux one. [ABSTRACT FROM AUTHOR]

The paper presents a study of issues related to the identification of a non-linear mathematical model describing dynamics of the temporomandibular joint (TMJ) disc. Based on the tests of real disks, a non-linear model was built and verified, and then numerical simulations were carried out, the purpose of which was to analyze the behavior of the model for various excitation conditions. They include, among others, plotting a multi-colored map of distribution of the largest Lyapunov exponent based on which the areas of occurrence of periodic and chaotic motion zones are identified. Bifurcation diagrams of steady states for sample sections of the Lyapunov map and phase flows of periodic and chaotic solutions are generated. For the same sections, numerical simulations are performed to identify coexisting solutions. These studies are carried out using diagrams showing the number of coexisting solutions and their periodicity. The research presented in the paper shows a very good match between the results of computer simulations and the data recorded in the laboratory experiment. Due to the very strong damping occurring in the system, the chaotic attractors resemble quasi-periodic solutions with their geometric shape. Strong damping also significantly affects multiple solutions, which are relatively rare in the analyzed model. Most of the chaotic responses and multiple solutions occur in the range of low amplitude values of the dynamic load affecting the tissues of the articular disc. The obtained results of numerical experiments clearly indicate that in the range of low frequency values of the external load acting on the system, single periodic solutions with a periodicity of 1 T dominate. With the increase of the load amplitude, the area of occurrence of such solutions increases. [Display omitted] • A novel non-linear mathematical model of the TMJ disk has been proposed. • The model was very well adjusted to the results of experimental studies. • The behavior of the model for chaotic and periodic motion zones was tested. • The presence of coexisting solutions was confirmed. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of the fully distributed fixed-time bipartite output consensus tracking for nonlinear heterogeneous multiagent systems (MASs) via both state-feedback and output-feedback methods under the switching topology. The adaptive fully distributed state observers with quantization information are designed to eliminate the dependence on the Laplacian matrix. For MASs with unknown model matrix, a novel fixed-time observer-based regulator equation is employed, which avoids repeatedly getting the unnecessary solution of universal one in the time-varying cooperation-competition communication topology. In this case, both fixed-time state-feedback and output-feedback controllers are constructed such that the output consensus tracking is achieved regardless the state value is available or unavailable. Besides, the upper bound of convergence time can be adjusted only by parameters without initial states. Lyapunov functions are established to derive conditions of achieving consensus tracking by mathematical analysis. Eventually, the effectiveness of the proposed control strategy is manifested by simulation results. [ABSTRACT FROM AUTHOR]

This paper considers a class of finite-time tracking problems of fractional-order uncertain system governed by nonlinear differential inclusion. We introduce a Lipschitz continuous condition into the set-valued mapping described by the closure of the convex hull of a set, and design P D γ -type and P I α D γ -type update laws with initial learning mechanisms in open loop and closed loop, respectively. Then, the Steiner-type selector and mathematical analysis tools are used to complete the convergence analysis. Finally, numerical examples are used to verify the validity of the theoretical results, and the tracking performance of system is compared for different values of γ , α and learning laws. [ABSTRACT FROM AUTHOR]

Time-varying problems frequently arise in the territories of science and engineering, and most of the time-varying problems can be described by dynamic matrix equations. As a powerful tool for solving dynamic matrix equations, the zeroing neural network (ZNN) develops fast in recent years. Convergence and robustness are two main performance indicators of the ZNN model. However, the development of the ZNN is focused on the improvement of its convergence in the past, and its robustness to noises is rarely considered. In order to achieve fast convergence and robustness of the ZNN model, a novel activation function (NAF) is presented in this paper. Based on the NAF, a noise-tolerant parameter-variable ZNN (NTPVZNN) model for solving dynamic Sylvester matrix equations (DSME) is realized, and its fixed-time convergence and robustness to noises are verified by rigorous mathematical analysis and numerical simulation results. Besides, two examples of electrical circuit currents computing and robotic manipulator trajectory tracking using the proposed NTPVZNN model in noisy environment further demonstrates its practical application ability. [ABSTRACT FROM AUTHOR]

The "Middle East Respiratory" (MERS-Cov) is among the world's dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model with a standard incidence rate is proposed to assess the role of media such as facebook, television, radio and tweeter in the mitigation of the outbreak of COVID-19. The basic reproduction number R 0 which is the threshold dynamics parameter between the disappearance and the persistence of the disease has been calculated. And, it is obvious to see that it varies directly to the number of hospitalized people, asymptomatic, symptomatic carriers and the impact of media coverage. The local and the global stabilities of the model have also been investigated by using the Routh–Hurwitz criterion and the Lyapunov's functional technique, respectively. Furthermore, we have performed a local sensitivity analysis to assess the impact of any variation in each one of the model parameter on the threshold R 0 and the course of the disease accordingly. We have also computed the approximative rate at which herd immunity will occur when any control measure is implemented. To finish, we have presented some numerical simulation results by using some available data from the literature to corroborate our theoretical findings. [ABSTRACT FROM AUTHOR]

• The paper is the first paper that provides a comprehensive theoretical analysis to the popular over-sampling method, SMOTE. • The theoretical and empirical analyses demonstrate the divergence of SMOTE patterns from the original minority distribution. • Our theoretical analysis applies to any data distribution, and we provide analysis for two examples of distributions. • We study the impact of number of minority patterns, dimensionality, and K of the KNN used in SMOTE, on SMOTE accuracy. • We study the impact of SMOTE in classification performance theoretically and empirically on LDA, KNN, and SVM classifiers. Imbalanced classification problems are often encountered in many applications. The challenge is that there is a minority class that has typically very little data and is often the focus of attention. One approach for handling imbalance is to generate extra data from the minority class, to overcome its shortage of data. The Synthetic Minority over-sampling TEchnique (SMOTE) is one of the dominant methods in the literature that achieves this extra sample generation. It is based on generating examples on the lines connecting a point and one its K -nearest neighbors. This paper presents a theoretical and experimental analysis of the SMOTE method. We explore the accuracy of how faithful it emulates the underlying density. To our knowledge, this is the first mathematical analysis of the SMOTE method. Moreover, we analyze the effect of the different factors on generation accuracy, such as the dimension, size of the training set and the considered number of neighbors K. We also provide a qualitative analysis that examines the factors affecting its accuracy. In addition, we explore the impact of SMOTE on classification boundary, and classification performance. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the mathematical analysis of a host–pathogen model with diffusion, hyperinfectivity and nonlinear incidence. We define the basic reproduction number ℜ 0 by the spectral radius of the next generation operator, and study the relation between ℜ 0 and the principal eigenvalue of the problem linearized at the disease-free steady state (DFSS). Under some assumptions, we show the threshold property of ℜ 0 : if ℜ 0 < 1 , then the DFSS is globally asymptotically stable (GAS), whereas if ℜ 0 > 1 , then the system is uniformly persistent and a positive steady state (PSS) exists. Moreover, for the special case where all parameters are constants, we show that the PSS is GAS for ℜ 0 > 1. Numerical simulation suggests that the spatial heterogeneity could enhance the intensity of epidemic, whereas the diffusion effect could reduce it. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a model-based rapid fault detection and isolation strategy using sliding mode observers. To address this problem, a new scheme is proposed by adaptively combining the information provided by a bank of observers. In this regard, a new structure for sliding mode observers is considered. Then, the well-known recursive least square algorithm is utilized to merge individual state estimations suitably such that the system fault is detected faster. The required condition for enhancing perfect state estimation is derived, and the stability of the overall system is proven via Lyapunov's direct method. The supremacy of proposed scheme is fully discussed through mathematical analyses as well as simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel opinion dynamics model grounded in the concept of bounded confidence interactions among agents. Our objective is to explain the polarization effects inherent to vector-valued opinions. The evolutionary process adheres to the rule where each agent aspires to increase polarization through communication with a single friend during each discrete time step. The friend is taken from a group of all agents in that way that his opinion is the target opinion of the considered agent. The introduced model can potentially explain the emergence of leaders or leading opinions within groups that actively pursue polarization as a central objective, including politics, fan clubs, and social networks. The dynamics ensure that agents' ultimate (temporal) configuration will encompass a finite number of outlier states. We introduce deterministic and stochastic models, accompanied by a comprehensive mathematical analysis of their inherent properties. Furthermore, we provide compelling illustrative examples and introduce a stochastic solver tailored for scenarios featuring an extensive set of agents. In the context of smaller agent populations, we scrutinize the suitability of neural networks for the rapid inference of limit configurations. [ABSTRACT FROM AUTHOR]

The correlation between an individual's activity level and the propagation of behavior is inherently intertwined on a social platform. Simultaneously, individuals with varying activity levels are subject to social reinforcement during the information accumulation process. In this paper, we develop a two-layer generalized Susceptible-Adopted-Recovered (SAR) model to simulate the cumulative effect of information reliability influenced by individual's activity and social reinforcement. Furthermore, we investigate how the accumulation of information reliability affects individual behavioral adoption. We provide a theoretical analysis of the mathematical model of the two-layer network based on edge-based compartmental theory and mean field theory. Subsequently, numerical simulations are performed to validate the model's effectiveness and offer insights for the advancement of information dissemination strategies. The results show that the proportion of active nodes in the network and their active intensities have a significant effect on behavioral propagation. The increase of them can reduce the outbreak threshold of behavioral adoption and expand the scale of behavioral adoption. Additionally, the intensity of local social reinforcement of information reliability has a more significant positive effect on behavioral adoption than global social reinforcement. Moreover, the information threshold of behavioral adoption in the Scale-Free (SF) network is larger than that in the Erdös-Rényi(ER) network. • A two-layer generalized Susceptible-Adopted-Recovered (SAR) model is proposed; • The information reliability is influenced by individual's activity and social reinforcement; • Both the proportion of active nodes and their intensities significantly affect behavioral propagation; • The intensity of local social reinforcement has a stronger positive impact on behavioral propagation; • The information threshold of behavioral adoption is compared in SF network and ER network. [ABSTRACT FROM AUTHOR]

A nonlinear cross-diffusion–fluid system with chemicals terms describing the dynamics of predator–prey living in a Newtonian fluid is proposed in this paper. The existence of weak solution for the proposed macro-scale system is proved on the basis of the Schauder fixed-point theory, a priori estimates, and compactness arguments. The proposed system is derived from the underlining description delivered by a kinetic-fluid theory model by multiscale approach. Finally, we discuss the computational results for the proposed macro-scale system in two dimensional space. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus tracking problems of singular partial differential multi-agent systems (SPD-MASs) with initial state errors under fixed and iteration-varying network topologies, where only certain follower agents have access the trajectory defined by virtual leaders. To solve this problem, a distributed iterative learning consensus protocol with initial state learning is proposed, ensuring accurate tracking of the leader's trajectory by all follower agents with initial state errors. The convergence conditions for consensus tracking error are derived through mathematical analysis between adjacent agents. Theoretical analysis shows that, under convergence conditions, the consensus error between any two agents can converge to zero along the iterative axis. Finally, numerical simulations show validate the effectiveness of the proposed distributed control protocol with initial state learning compared to traditional protocols without state learning. [ABSTRACT FROM AUTHOR]

Economics and finance are extremely complex nonlinear systems involving human subjects with many subjective factors. There are numerous attribute properties that cannot be described by the theory of integer-order calculus; so it is necessary to theoretically study the internal complexity of the economic and financial system using the method of bifurcation and chaos of fractional nonlinear dynamics. Fractional calculus can more accurately describe the existence characteristics of complex physical, financial or medical systems, and can truly reflect the actual state properties of these systems; therefore the application of fractional order in chaotic systems has great significance to study the mathematical analysis of nonlinear dynamic systems, and the use of fractional calculus theory to model the complexity evolution of fractional chaotic financial systems has attracted more and more scholars' attention. On the basis of summarizing and analyzing previous studies, this paper qualitatively analyzes the stability of equilibrium solution of fractional-order chaotic financial system, and explores the complexity evolution law of the financial system near the equilibrium point and the occurring conditions of asymptotic chaotic state near this equilibrium point, and simulate the complexity evolution of chaotic financial systems using the Admas-Bashforth-Moulton finite difference method for mapping, phase diagram and time series graph. The research results of this paper provide a reference for government to formulate relevant economic policies, decision-making or further research on the complexity evolution of fractional-order chaotic financial systems. [ABSTRACT FROM AUTHOR]

• Fractional Adams–Bashforth schemes for Atangana–Baleanu–Caputo operators. • Fixed point theory for existence and uniqueness of solution. • Mathematical analysis and numerical simulations. • Chaotic patterns in symbiosis dynamics. Research findings have shown that evolution equations containing non-integer order derivatives can lead to some useful dynamical systems which can be used to describe important physical scenarios. This paper deals with numerical simulations of multicomponent symbiosis systems, such as the parasitic predator-prey model, the commensalism system, and the mutualism case. In such models, we replace the classical time derivative with either the Caputo fractional derivative or the Atangana-Baleanu fractional derivative in the sense of Caputo. To guide in the correct choice of parameters, we report the models linear stability analysis. Numerical examples and results obtained for different instances of fractional power α are provided for non-spatial models as well as the spatial case in one and two dimensions in other to justify our theoretical findings which include the chaotic phenomena, spatiotemporal and oscillatory patterns, multiple steady states and other spatial pattern processes. This paper further suggest an alternative approach to incessant killing of wildlife animals for pattern generation and decorative purposes. [ABSTRACT FROM AUTHOR]

Abstract It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an alternative approach: the smaller of two input random numbers is divided by the larger, resulting in a rational number from [ 0 , 1 ]. We investigate some basic theoretical properties of this approach and show that it yields a good approximation to the ideal uniform distribution. The focus of this paper, however, is on the empirical performance of the new transformation when applied to different generators. For a thorough statistical evaluation, we use the well-known test suite TestU01 (see L'Ecuyer and Simard, 2007). We apply the ratio transformation to moderately bad generators, i.e. those that failed up to 40% of the tests from the test battery Crush of TestU01. We show that more than half of them turn into empirically very good generators that pass all tests of Crush and BigCrush from TestU01 when the ratio transformation is applied. In particular, generators based on linear operations seem to benefit from the ratio, as this breaks up some of the unwanted regularities in the input sequences. Thus the additional effort to produce a second random number and to calculate the ratio allows to increase the quality of available random number generators, at least in a statistical sense. [ABSTRACT FROM AUTHOR]

Abstract The goal of this paper is to propose an optimal fault tolerant control (FTC) approach for multi-agent systems (MASs). It is assumed that the agents have identical affine dynamics. The underlying communication topology is assumed to be a directed graph. The concepts of both inverse optimality and partial stability are further employed for designing the control law fully developed in the paper. Firstly, the optimal FTC problem for linear MASs is formulated and then it is extended to MASs with affine nonlinear dynamics. To solve the Hamilton-Jacobi-Bellman (HJB) equation, an Off-policy Reinforcement Learning is used to learn the optimal control law for each agent. Finally, a couple of numerical examples are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems. [ABSTRACT FROM AUTHOR]

Highlights • The paper deals with the existence of nonlinear fractal interpolation surfaces (FISs). • We apply the Geraghty's fixed point theorem to the existence of the FISs. • We establish new theorems under weaker assumptions. • Explicit examples are given to illustrate the main results. Abstract In this paper we present new methods to generate fractal interpolation surfaces which generalize the existing fractal interpolation surfaces. We ensure that attractors of nonlinear iterated function systems constructed by Geraghty contractions are graphs of some continuous functions which interpolate the given data. In particular, we give two explicit illustrative examples to demonstrate the effectiveness of obtained results. [ABSTRACT FROM AUTHOR]

This paper aims to suggest a time-fractional S P E P I P A I P S P H P R P model of the COVID-19 pandemic disease in the sense of the Atangana–Baleanu–Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam–Hyers and the generalized Ulam–Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik–Atangana numerical scheme, which validates the importance of arbitrary order derivative ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method for 3D human joint estimation using part segmentation, and introduce an application for size measurement based on the obtained joints. A human segmentation dataset is first prepared as training set for the advanced neural network architecture. Different human parts yielded from the neural network are utilized to extract human joints. In the proposed method, the joints are categorized into the active joints and inert joints. In the extraction process of the active joints, the mathematical analysis method is adopted to calculate the joint positions. The geometric features of different human segments are further used to extract the inert joints. Moreover, we test on the dataset to compare its performance with our previous method based on geometrical features. The results show the average error of the joints is less than 4.2 cm, which is significantly improved from 5.8 cm demonstrated in our previous research. We also investigate the human size measurement. The distance between the joints is used to calculate the length, and the ellipse fitting method based on multi-frame point cloud is adapted to calculate the human girths. Compared with the manual measurement data, the size error is less than 4.1 cm. [ABSTRACT FROM AUTHOR]

In the framework of several nonlinear physical phenomena arising from water wave mechanics, this work recovers some new precise solutions to the time-fractional phi-four equation. For this, the phi-four equation's space and time fractional transformation is converted into an ordinary differential equation (ODE). The improved modified extended tanh function (imETF) approach is then employed by the ODE as a powerful method based on the conformable derivative. Thus, lump solutions, periodic solutions, solitary and multiple soliton solutions, dark-bright soliton solutions, and Jacobi elliptic doubly periodic type solutions are studied. The imETF appro solitons applications in many scientific and engineering fields develops mathematical methodologies, helps research solitons, and advances our knowledge of nonlinear processes. The differences between the results of this investigation and those obtained earlier using alternative methods are analyzed. In terms of fractionality, unconstrained parameters, and applied method sense, all generated wave solutions are found to be new. Physical explanations and a visual representation of the effects of unconstrained parameters and fractionality on the derived solutions are provided. We find that the wave portents change as the number of unconstrained parameters and fractionality increases. In conclusion, we dynamically show that the proper transformation and the applicable imETF method are more effective in analyzing water wave dynamics and might be employed in subsequent studies to shed light on various physical phenomena. • This paper discusses the dynamical behaviour of solitary waves for the time-fractional phi-four equations. • The improved modified tanh-function (imETF) method has been used to determine the wave structure. • Several hyperbolic and Jacobi elliptic doubly periodic type solutions have been observed. • Several 3D shapes have been obtained, including singular, double, multiple solitons, lump, kink, cusp, dark solution, etc. • We hope our results will be helpful for applied sciences in future studies. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L 2 − L ∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (C S T R). [ABSTRACT FROM AUTHOR]

An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]

Problems of anisotropic functionally graded media which are governed by the transient diffusion–convection–reaction equation of spatially varying coefficients are discussed in this paper. A mathematical analysis is used to transform the variable coefficient equation into a constant coefficient equation. A boundary-only integral equation is then derived from this constant coefficient equation after being Laplace transformed. Numerical solutions to the problems are sought by using a boundary element method (BEM) which is combined with the Stehfest formula for the numerical Laplace transform inversion. Some problems considered are those of compressible or incompressible flow, and of media which are quadratically, exponentially or trigonometrically graded materials. The results obtained show that the analysis used to transform the variable coefficients equation into the constant coefficients equation is valid, and the mixed LT-BEM is easy to implement and accurate for finding numerical solutions. The numerical solutions of some test problems are justified by showing their accuracy. Some non-test problems of geometrically symmetric systems are also considered to show the effect of the anisotropy and inhomogeneity of the material on the solutions by verifying the symmetry of solutions. In addition, the effect of boundary conditions is also exhibited. [ABSTRACT FROM AUTHOR]

In the paper, we describe the new measure of matching fuzzy sets. The introduced measure of perturbation of one fuzzy set by another fuzzy set is considered instead of commonly used distance between two fuzzy sets. The operations known in the fuzzy set theory are used and the perturbation of one fuzzy set by another fuzzy set is understood as a measure describing changes of the first fuzzy set after adding the second one. Obviously, the opposite case can also be considered wherein the second fuzzy set is perturbed by the first one. In general, the new measure is asymmetric and can provide more information compare to a distance between fuzzy sets. The values of such measures of fuzzy sets’ perturbation are in range between 0 and 1. In this paper several mathematical properties of the measure of fuzzy sets’ perturbation are studied, and the measure of sets’ perturbation is compared to other selected measures. [ABSTRACT FROM AUTHOR]

A novel messages spreading model is suggested in this paper. The model is a natural generalization of the SIS (susceptible-infective-susceptible) model, in which two relevant messages with same probability of acceptance may spread among nodes. One of the messages has a higher priority to be adopted than the other only in the sense that both messages act on the same node simultaneously. Node in the model is termed as supporter when it adopts either of messages. The transition probability allows that two kinds of supports may transform into each other with a certain rate, and it varies inversely with the associated levels which are discretely distributed in the symmetrical interval around original point. Results of numerical simulations show that individuals tend to believe the messages with a better consistency. If messages are conflicting with each other, the one with higher priority would be spread more and another would be ignored. Otherwise, the number of both supports remains at a uniformly higher level. Besides, in a network with lower connected degree, over a half of the individuals would keep neutral, and the message with lower priority becomes harder to diffuse than the prerogative one. This paper explores the propagation of multi-messages by considering their correlation degree, contributing to the understanding and predicting of the potential propagation trends. [ABSTRACT FROM AUTHOR]

Stabilization of a coupled linear plant and reaction–diffusion process by boundary control was considered in a paper by Zhao and Xie. In this paper, backstepping transformation with a kernel function and a vector-valued function was introduced to design a control law. For the situation without heat resource in the reaction–diffusion process, the kernel function and the vector-valued function in the transformation had been obtained, and the explicit control law had been established. However, for the reaction–diffusion process with heat resource, the explicit solutions of the kernel function and the vector-valued function in the transformation have not been obtained. Thus, an explicit control law has not been established. In the present paper, the explicit solutions of the kernel function and the vector-valued function in the transformation are obtained through some mathematical skills and complicated computation, and the explicit control law has been established. [ABSTRACT FROM AUTHOR]

In this paper, a new SIS (susceptible–infected–susceptible) epidemic model on complex networks with an infective medium is proposed. The infection rate is modified by applying the theory of probability. By using mean-field approximation, iterative analysis method and mathematical analysis, the epidemic threshold, stabilities of the disease-free equilibrium and the endemic equilibrium are studied. Moreover, some disease control strategies are proposed. The results show that the epidemic threshold plays an important role in the spread of disease. Finally, the theoretical results are confirmed by some simple numerical examples. [ABSTRACT FROM AUTHOR]

As a typical methodology to deal with uncertain issues, the three-way decision (3WD) has been developed rapidly in nearly ten years, both in theories and applications. Three-way classification is one of the important research fields of 3WD, which utilizes the idea of 3WD to solve classification problems. In this paper, we focus on investigating the effectiveness of three-way classification through two evaluation indicators: the classification quality (Precision , Recall , Accuracy and F 1 ) and the decision cost. The comparisons between two-way classification and three-way classification are concretely analyzed, some mathematical properties, judging conditions and decision criteria of these two classification methods are also discussed in detail. Finally, the experimental results on eight UCI data sets validate the mathematical analysis, which reveal the effectiveness of three-way classification. [ABSTRACT FROM AUTHOR]

Substance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including opioid use disorder developed through prescription use and alcoholism developed primarily due to genetic factors or stress, depression, and other psychological factors. In this paper we will demonstrate that even a simple infectious disease model is structurally unstable with respect to a linear perturbation in the infection term — precisely the sort of term necessary to model SUD development in isolation. This implies that models of SUD which exclusively treat problematic substance use as an infectious disease will have misleading dynamics whenever a non-trivial rate of isolated SUD development exists in actuality. As we will show, linearly perturbed SUD models do not have a use disorder-free equilibrium. To investigate management strategies, we implement optimal control techniques with the goal of minimizing the number of SUD cases over time. • Advancement in structural theory for epidemiological models of substance use disorder. • Models with non-contact infectivity form fundamentally different resulting dynamics. • Developed a framework to find feasible management methods for substance use disorder. • Use of optimal control in the context of a disease with multiple modes of infectivity. [ABSTRACT FROM AUTHOR]

Vegetation patterns can reflect vegetation's spatial distribution in space and time. The saturated water absorption effect between the soil–water and vegetation plays a crucial role in the vegetation patterns in semi-arid regions. Moreover, vegetation can absorb water through the nonlocal interaction of roots. In this paper, we consider how cross-diffusion and nonlocal delay interactions affect vegetation growth. The conditions under which the vegetation-water model generates the Turing pattern are obtained by mathematical analysis. At the same time, the multiple scales method is applied to obtain the amplitude equations at the critical value of Turing bifurcation, which helps us to derive parameter space more specifically where specific patterns such as strips, hexagons, and the mixture of strip and hexagons will emerge. Various spatial distributions of vegetation in semi-arid areas are qualitatively depicted by numerical simulations. The results show that the nonlocal delay effect enhances vegetation biomass. Therefore, we can take measures to increase the intensity of the nonlocal delay effect to increase vegetation density, which theoretically provides new guidance for vegetation protection and desertification control. • We consider a spatial vegetation system with cross-diffusion and nonlocal delay. • The nonlocal water absorption intensity can induce the phase change of vegetation pattern. • Regular spot, stripe and mixed patterns appear in the appropriate feedback intensities. [ABSTRACT FROM AUTHOR]

Different from the existing iterative learning control (ILC) works for dynamical systems with iteration-varying trial lengths, in which the terminal time points are not identical, this paper presents an ILC approach for linear discrete time-varying (LDTV) systems with different initial time points. A piecewise ILC law is designed by using the segment compensation techniques in time axis. Through a rigorous mathematical analysis, it is theoretically proved that as the mathematical expectation of the iterative initial state equals to the desired initial state, the ILC tracking error at the maximum universal time interval can be driven into a bounded region in mathematical expectation sense. Particularly, the mathematical expectation of the ILC tracking error at the maximum universal time interval can even be driven to zero under a certain initial state condition. Numerical simulations are provided to verify the effectiveness of the proposed ILC scheme. [ABSTRACT FROM AUTHOR]

In this paper, we study a variable-order fractional mathematical model driven by Lévy noise describing the new variant of COVID-19 (Omicron virus). Based on our analysis and discussion under a new set of sufficient conditions, we prove the existence and uniqueness of the related solution. Moreover, we discuss the stability analysis of the corresponding Omicron virus model by employing Ulam–Hyers and Ulam–Hyers–Rassias stabilities in Banach spaces. Finally, we present some numerical results and comparative studies to show clearly the importance of our results and its effects on behaviors of the new variant model. • Our paper presents a fractional mathematical model describing the new variant of SARS-CoV-2. • We prove the existence of the unique solution under a new set of suitable conditions. • We discuss Ulam–Hyers stability for the corresponding model. • We provide some numerical results to show clearly the importance of our study. • Our findings improve and generalize some works concerning the new variant Omicron model. [ABSTRACT FROM AUTHOR]

Whether the pension system transition is successful is closely related to the accurately accounted IPD amount and rationally solved scheme. China faces the problem of IPD with no exception. This paper uses individual cost method theory, combining Chinese pension system and its operation, builds up the implicit pension debt calculation model, then it measures the Chinese IPD quantity by statistical data. The paper finds out that the average IPD per-year is 39.404 billion Yuan in 2013–2050, the maximum is 185.053 in 2022, the minimum is 0.150 in 2050, and the accumulative IPD will sustain growth with annual growth rate of 7.06% in 2013–2050, from 119.787 billion Yuan to 1497.337 billion Yuan. Finally, this paper proposes the government to raise the legal retirement age, reduce the pension substitution rate, expand the coverage of endowment insurance, improve the investment yield of the pension fund, and so on, to compensate the IPD in China. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of fractional initial value problems (FIVP) in sense of Caputo’s definition for dynamical systems. Unlike for integer-order derivatives that have a single definition, there is more than one definition of non integer-order derivatives and the solution of an FIVP is definition-dependent. In this paper, the chief differences of the main definitions of fractional derivatives are revisited and a numerical algorithm to solve an FIVP for Caputo derivative is proposed. The main advantages of the algorithm are twofold: it can be initialized with integer-order derivatives, and it is faster than the corresponding standard algorithm. The performance of the proposed algorithm is illustrated with examples which suggest that it requires about half the computation time to achieve the same accuracy than the standard algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a unified matrix upper solution bound is established for the continuous coupled algebraic Riccati equation arising from the optimal control of a Markovian jump linear system. In particular, the issue of rank deficiency with the control matrices is addressed because it may cause problems to some existing matrix upper solution bounds. The results of this paper not only apply to this rank deficient case but also contain those existing results as special cases. [ABSTRACT FROM AUTHOR]

In this paper the comparison of a proposed neural network with generalized type-2 fuzzy weights (NNGT2FW) with respect to the monolithic neural network (NN) and the neural network with interval type-2 fuzzy weights (NNIT2FW) is presented. Generalized type-2 fuzzy inference systems are used to obtain the generalized type-2 fuzzy weights and are designed by a strategy of increasing and decreasing an epsilon variable for obtaining the different sizes of the footprint of uncertainty (FOU) for the generalized membership functions. The proposed method is based on recent approaches that handle weight adaptation using type-1 and type-2 fuzzy logic. The approach is applied to the prediction of the Mackey–Glass time series, and results are shown to outperform the results produced by other neural models. Gaussian noise was applied to the test data of the Mackey–Glass time series for finding out which of the presented methods in this paper shows better performance and tolerance to noise. [ABSTRACT FROM AUTHOR]

The problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both NP-hard problems. This paper studies the relationship between the two problems. The vertex cover problem for graphs from the perspective of rough sets is first investigated. The attribute reduction of an information system is then studied in the framework of graph theory. The results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph. Conversely, the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph. Finally, a new algorithm for the vertex cover problem based on rough sets is presented. Furthermore, experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones. [ABSTRACT FROM AUTHOR]