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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]

In this paper, the numerical properties of a nonlinear age-structured hepatitis B virus model with saturated incidence and spatial diffusion are studied. Applying linearly implicit Euler method in time integration, a numerical scheme which can preserve the biological meanings is constructed. The convergence of the numerical solution in finite time is explored. In stability analysis, a threshold is proposed, which is called numerical basic reproduction number and denoted by R 0 h. It is proved that the numerical solution is locally asymptotically stable at the disease-free equilibrium when R 0 h < 1. Moreover, it is proved the numerical basic reproduction number converges to the exact basic reproduction number of the model with first order accuracy. Furthermore, it is shown that a numerical space independent equilibrium exists and is asymptotically stable if R 0 h > 1 , which implies the threshold stability of the model can be preserved by numerical solution proposed. Eventually, our conclusions are tested through numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

In ecosystems, cooperative behavior is universal and can dramatically improve a species' chances of survival. Nevertheless, the situations that can occur when different species with cooperative tendencies interact are veiled. To explore such a situation, in this paper, we investigate how cooperative behavior can affect biodiversity in the population system. Based on the spatial rock–paper–scissors (RPS) game, which incorporates the relative power between predator and prey species, we redefine the competition rate to facilitate cooperative behavior. Competition rates are modulated by the sensitivity parameter, which regulates alterations in competition rates stemming from variations in predator–prey population disparities. Through comprehensive numerical analysis, we have demonstrated compelling evidence confirming the nature of cooperative behavior in maintaining biodiversity. The sensitivity parameter acts as a double-edged sword; it hampers biodiversity when it falls below a certain level. Conversely, when it exceeds the threshold, it supports the maintenance of biodiversity. From snapshots and the coefficient analysis based on spatial autocorrelation, we found that empty sites are essential to promote coexistence as resource nodes. Compared with previous studies in spatial RPS games, our findings suggest that simple modification of a competition rate rather than exploiting cooperative games can realize the cooperative behavior of cyclically competing populations, and biodiversity is sensitively affected by cooperation. • We define cooperative behavior between species by redefining competition rates. • Cooperation affects competition and exchange sensitively, affecting biodiversity. • Empty spaces play an important role and are crucial in promoting coexistence. [ABSTRACT FROM AUTHOR]

Computer viruses present a substantial threat to our daily lives. Traditional models for the propagation of computer viruses primarily concentrate on network structures. In this paper, we take into account the constrained availability of resources in the context of computer virus prevention and control. We introduce a computer virus propagation model based on resource limitations. By examining the stability of both toxic and non-toxic equilibria within the model, we employ Matlab and Python for numerical analysis to simulate various computer virus propagation scenarios. Additionally, we present corresponding defense mechanisms for combatting these viruses. [ABSTRACT FROM AUTHOR]

We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper. • Convergence of a spectral method for a peridynamic formulation of Richards' equation. • Existence and uniqueness of the solution by its stability and compactness properties. • Simulations to numerically verify the existence of the weak solution to the model. [ABSTRACT FROM AUTHOR]

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random free boundary partial differential problem and it is addressed numerically combining the finite difference method with two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical examples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties of the schemes and show the numerical convergence. [ABSTRACT FROM AUTHOR]

The acquisition of drinking water is discussed in this paper by three-dimensional modeling of a solar desalination plant focusing on renewable energies. The reservoir of the desalination plant contains aluminum nanoparticles with a constant weight percent. A layer of n-Eicosane phase change material (PCM) with various thicknesses is used at the bottom of the desalination plant reservoir. The objective of the present paper is to examine the entropy generation, including frictional, thermal, and total entropy generation in the flow of steam and air inside the desalination plant and the use of the PCM layer. The angle of the glass changes from 10 to 45°, and the thickness of the PCM layer varies during the day. The nanofluid flow is assumed to be two-phase, and the finite element method (FEM) is employed to solve the equations using COMSOL software. The results show that increasing the glass angle enhances the frictional entropy generation, and decreases the thermal entropy generation. Using PCM with a thickness of 50 mm reduces the thermal entropy generation in the steam, especially in the afternoon. The amount of PMC thickness changes the total entropy generation in the PMC. [ABSTRACT FROM AUTHOR]

This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize electrostatic forces to actuate elastic surfaces. The potential equilibrium states of MEMS are described by solutions of a singularly perturbed elliptic nonlinear PDE. We develop a numerical method which couples a finite element approximation with mesh refinement to a pseudo arc-length continuation algorithm to numerically obtain bifurcation diagrams in the physically relevant two dimensional scenario. Several geometries, including a unit disk, square, and annulus, are studied to understand the behavior of the system over a range of domains and parameter regimes. We find that solution multiplicity, and importantly the potential for bistability in the system, depends sensitively on the parameters. In the annulus domain, symmetry breaking bifurcations are located and asymmetric solution branches are tracked. This work significantly extends the envelope for numerical characterization of equilibrium states in microscopic electrostatic contact problems relating to MEMS. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the unsteady incompressible thermomicropolar fluid (UITF) equations are considered. Theoretically, some a priori regularity conclusions are presented firstly, which seem to be not available in the literatures. Numerically, a penalty finite element method (PFEM) for the UITF equations is studied, the Euler semi-implicit temporal semi-discrete method of the penalty UITF equations is proposed, the stability and the L 2 - H 1 error estimates of the temporal discrete solutions are proved. Finally, the stability and the L 2 - H 1 error estimates for the finite element fully-discrete approximation of the penalty UITF equations are rigorously proved. The accuracy and efficiency of the fully-discrete PFEM are demonstrated by some numerical examples. • This paper focus on penalty method for unsteady incompressible thermomicropolar fluid equations. • Some a priori regularity conclusions are presented. • Stability and L 2 − H 1 error estimates of Euler semi-implicit method are proposed. • Stability and L 2 − H 1 error estimates of fully-discrete method are proved. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective Chebyshev–Picard iteration (CPI) method for solving delay differential equations with a constant delay. This approach adopts the Chebyshev series to represent the solution and improves the accuracy of the solution by successive Picard iterations. The CPI method is implemented in a matrix–vector form efficiently without matrix inversion. We also present a multi-interval CPI method for solving long-term simulation problems. Further, the convergence of the CPI method is analyzed by evaluating the eigenvalues of the coefficient matrices of the iteration. Several numerical experiments including both the linear and nonlinear systems with delay effects are presented to demonstrate the high accuracy and efficiency of the CPI method by comparison with the classic methods. [ABSTRACT FROM AUTHOR]

Artificial neural networks, celebrated for their human-like cognitive learning abilities, often encounter the well-known catastrophic forgetting (CF) problem, where the neural networks lose the proficiency in previously acquired knowledge. Despite numerous efforts to mitigate CF, it remains the significant challenge particularly in complex changing environments. This challenge is even more pronounced in cross-domain adaptation following the continual learning (CL) setting, which is a more challenging and realistic scenario that is under-explored. To this end, this article proposes a cross-domain CL approach making possible to deploy a single model in such environments without additional labelling costs. Our approach, namely continual learning approach for many processes (CLAMP), integrates a class-aware adversarial domain adaptation strategy to align a source domain and a target domain. An assessor-guided learning process is put forward to navigate the learning process of a base model assigning a set of weights to every sample controlling the influence of every sample and the interactions of each loss function in such a way to balance the stability and plasticity dilemma thus preventing the CF problem. The first assessor focuses on the negative transfer problem rejecting irrelevant samples of the source domain while the second assessor prevents noisy pseudo labels of the target domain. Both assessors are trained in the meta-learning approach using random transformation techniques and similar samples of the source domain. Theoretical analysis and extensive numerical validations demonstrate that CLAMP significantly outperforms established baseline algorithms across all experiments by at least 10% margin. • This paper presents a scarcely addressed problem, cross-domain continual learning. • This paper proposes a new algorithm, continual learning approach for many processes (CLAMP), for cross-domain continual learning. • Extensive numerical validations and theoretical studies are performed to guarantee the advantage of CLAMP. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical representation of the linearly implicit Euler method for an age-structured HIV infection model with a general transmission mechanism. We first define the basic reproduction number of the continuous model, and present the stability results of the equilibriums. For the numerical process, we establish the solvability of the system and the non-negativity and convergence of numerical solutions. In the analysis of the long-term dynamical behavior, this paper mainly focus on the existence of the infection equilibrium determined by the numerical reproduction number R 0 Δ t. To overcome the difficulty caused by the complexity of epidemic transmission mechanisms, the 1-order convergence analysis of numerical basic reproduction numbers R 0 Δ t is implemented by using the properties of the fundamental solution matrix. By a comparison principle, we show that the disease-free equilibrium is globally asymptotically stable if R 0 Δ t < 1. Moreover, for R 0 Δ t > 1 , a unique numerical endemic equilibrium exists, which converges to the exact one, is locally asymptotically stable. Hence, numerical processes visually represent the dynamic properties of nonlinear age-structured HIV models. Finally, some numerical experiments demonstrate the verification and the efficiency of our results. • The age-structured HIV model with general transmission is reviewed. • The exact basic reproduction number is recalled. • The linearly implicit Euler method is implemented to the model. • The theoretical and numerical threshold dynamics are investigated. • The convergence of the basic reproduction numbers is proved for general case. [ABSTRACT FROM AUTHOR]

Conventional data compression schemes aim at implementing a trade-off between the rate required to represent the compressed data and the resulting distortion between the original and reconstructed data. However, in more and more applications, what is desired is not reconstruction accuracy but the quality of the realization of a certain task by the receiver. In this paper, the receiver task is modeled by an optimization problem whose parameters have to be compressed by the transmitter. Motivated by applications such as the smart grid, this paper focuses on a goal function which is of L p -norm-type. The aim is to design the precoding, quantization, and decoding stages such that the maximum of the goal function obtained with the compressed version of the parameters is as close as possible to the maximum obtained without compression. The numerical analysis, based on real smart grid signals, clearly shows the benefits of the proposed approach compared to the conventional distortion-based compression paradigm. • General framework for designing compression methods for the L p norm minimization problem. • Novel linear and nonlinear transformation schemes by taking into account the performance degradation in terms of the L p norm induced by model reduction. • Tailor the quantization rule to be goal-oriented by considering the impact of the precoding and the final use of the compressed data. • Evaluation of the proposed coding schemes with a real dataset and show the significant performance improvement compared to existing conventional transformation and quantization techniques. [ABSTRACT FROM AUTHOR]

The PVT solar collectors can produce the thermal energy and power in a same frame. The improvement of the PVT's efficiency leads to reducing the system size and capital costs. To this end, this paper studied the irreversibilities of the Al 2 O 3 Cu/water hybrid nanofluid (NF) in a PVT solar collector considering two single and double serpentine channels (SS and DS). The influences of Re and nanoparticle concentration (φ) on the thermal and frictional entropy generation rates (S ˙ t h and S ˙ f r) were investigated and the thermal, electrical and overall exergy efficiencies (ψ th , ψ e , ψ ov) of the PVT with SS and DS channels were compared and discussed. Based on the results, the DS channel exhibited S ˙ f r of almost 75 % lower than SS channel due to lower nanofluid inlet velocities and velocity gradients. In addition, S ˙ t h for the DS channel is nearly 65 % lower and 26 % higher than that for the SS channel at Re numbers of 500 and 2000, respectively. Besides, the Re escalation from 500 to 2000 intensifies S ˙ f r by almost 94 % at different φs in the SS and DS channels. The increase in φ from 0 % to 1 % escalates S ˙ f r by almost 99.98 % times for two configuration regardless of the Re number. ψ th of the DD channel is nearly 14.5 % and 12.77 % higher than that of the SS channel at Re s of 500 and 2000, respectively. Besides, ψ e of the PVT with the DS channel is 2.36 % higher than that with SS channel at Re =500 at four studied φs. Moreover, the maximum ψ e for the PVT with the DS and SS were obtained as 22.29 % and 21.28 %, respectively, which are associated with Re =1500 and φ=0.25 %. Additionally, a predictive model was presented to determine the total entropy generation rate based in the Re and φ as the inputs. [ABSTRACT FROM AUTHOR]

This paper studied the heat transfer and entropy generation rate of water-Fe 3 O 4 magnetic nanofluid flow inside three twisted tubes with square, triangular, and elliptical cross-sections at the absence and presence of a magnetic field (MF) effect for Reynolds number (Re) range of 400–800, pitch distance (P s) range of 25–75 mm as well as the nanoparticle concentration (φ) range of 1%, 2%, and 4%. Based on the results, the increase in Re from 400 to 800 escalated convective heat transfer coefficient (h) by 33.98% (or 4.66%), 23.97% (or 18.46%) and 31.36% (or 20.91%) in the square, triangular, and elliptical twisted tubes, respectively, under the absence (or presence) of the MF. At P =50 mm and φ=2%, the MF improved h by 21–45%, 21–26%, and 0–16% within the Re range of 400–800 for the square, triangular, and elliptical twisted tubes, respectively. Nearly 60% and 50% pressure drop observed as Re escalated from 400 to 800 in the absence and presence of the MF, respectively. The highest performance evaluation criterion (PEC) (i.e. 1.45) and the lowest PEC (i.e. 0.91) were obtained for the square twisted tube at Re =400 and elliptical tube at Re = 800, respectively. The highest and lowest PEC of the square twisted tube (i.e. 1.88 and 1.45) at Re =400 were observed for P =50 mm and φs of 4% and 2%, respectively. In the presence of the MF effect, nearly 37–48% (or 32–35%) increase in the S ˙ f r (or S ˙ t h) were obtained at P s of 25–75 mm against the cases without the MF effect. [ABSTRACT FROM AUTHOR]

In this paper, a novel COVID-19 reaction–diffusion model with virus mutation and media coverage is investigated. First, the solution's uniform boundedness for the system is established. Then, the basic reproduction numbers for ordinary and mutant viruses spread in heterogeneous environments are defined. Furthermore, the endemic equilibrium's asymptotic distribution for the system is explored. In addition, when one diffusion coefficient tends to zero and the other diffusion coefficients are greater than zero and fixed, the solution of the system will asymptotically approach endemic equilibrium. Next, a theoretical analysis of how high-frequency media coverage affects the development of the COVID-19 epidemic is conducted. Theoretical research shows that high-frequency media coverage will lead to the disappearance of the disease. Meantime, global sensitivity analysis on the basic reproduction numbers R 01 and R 02 are performed. Finally, theoretical simulations and instance predictions are carried out. Because of the complexity of the Shanghai epidemic and changes in management and control, the infection rates β 1 (t) , β 2 (t) are given in the form of a piecewise function with more practical significance, and they are used to predict the epidemic trend of COVID-19 in Shanghai. Through a series of numerical simulations and analysis, the key indicators of the Shanghai COVID-19 epidemic are as follows : (1) The basic reproduction numbers in the early, middle, and late stages of COVID-19 are R ¯ 0 (1 : 34) = 0. 9152 , R ¯ 0 (35 : 49) = 3. 1476 , and R ¯ 0 (50 : 140) = 0. 6547 , respectively; (2) This epidemic round in Shanghai will peak at 3,270 new daily confirmed cases on the 49th day (April 15); (3) The final size of the epidemic will reach 63,470 confirmed cases; (4) This round of COVID-19 epidemic in Shanghai, China, is expected to be fully cleared in late June to early July. The above conclusions are basically consistent with the facts. Of course, with the rise in temperature and strict control, the epidemic situation in Shanghai, China, is expected to be cleared earlier. Our results provide new ideas for preventing and controlling the COVID-19 epidemic. • A reaction–diffusion model with virus mutation and media coverage is proposed. • The asymptotic properties of endemic equilibrium with small diffusion are explored. • Global sensitivity analysis for R 01 and R 02 and are performed. • Applying piecewise functions β 1 (t) , β 2 (t) , to predict the Shanghai COVID-19 epidemic. • Key indicators of COVID-19, such as R 0 , peak, final scale, clear time are obtained. [ABSTRACT FROM AUTHOR]

In a recent paper [H. Dong, J. Tang, and X. Mao, SIAM J. Control Optim., 2022], the stability of delayed feedback control of Lévy noise driven stochastic delay hybrid systems is discussed. Notably, the system assumes the absence of the neutral term and imposes the classical linear growth condition on the jump coefficients. This work aims to close the gap by imposing the superlinearly growing jump coefficients for a class of highly nonlinear neutral stochastic delay hybrid systems with Lévy noise (NSDHSs-LN), where neutral-term implies that the systems depend on derivatives with delays in addition to the present and past states. We first show the existence and uniqueness theorem of the solution to the highly nonlinear NSDHSs-LN under the local Lipschitz condition, along with the moment boundedness and finiteness of the solution. We then demonstrate the moment exponential stability and almost sure exponential stability of highly nonlinear NSDHSs-LN through a variable-delay feedback control function and Lyapunov functionals. Finally, we apply our results to a concrete stabilization problem of a coupled oscillator-pendulum system with Lévy noise, and some numerical analyses are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The application of V-cut twisted tape turbulator inserted in the absorber tube of a photovoltaic thermal (PVT) system was investigated through a 3-D numerical analysis. The objective was to determine the effect of turbulator pitch distance (50 mm, 77 mm, and 100 mm) and Re number (500, 1000, 1500, and 2000) on the PVT energy and exergy performances. The results were compared with those obtained for the absorber tube without turbulator. Our findings demonstrated that the pressure drop and PV temperature, respectively, escalates and diminishes by 78–84% and 5.69–6.68% for the case with turbulator (pitch of 100 mm) as Re increases from 500 to 2000. In consequence, the overall energy efficiency and overall exergy efficiency improve by 15.76–14.27% and 12.01–8.68%, respectively, for the increase in Re within the studied range. In addition, the application of turbulator with a pitch of 100 mm improves the overall energy and exergy efficiencies of the PVT system by 3.04–7.70% and 4.03–13.08% at the Re range of 500–2000 as compared to the without turbulator case. Moreover, the greatest useful thermal and electrical efficiencies were obtained for the PVT with turbulator pitch of 100 mm and at Re =2000, which yields the highest overall thermal and exergy efficiencies of 75.46% and 16.34%, respectively. Furthermore, RSM technique is utilized to obtain a model for the overall energy and exergy efficiencies versus Re and P. [ABSTRACT FROM AUTHOR]

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ ∈ (0 , 1 ] , we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O (h m + ɛ τ 2) up to the long time at O (1 / ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the high-order approximation of a class of SPDEs with cubic nonlinearity driven by multiplicative noise with the help of the amplitude equations. The highlight of our work is the provision of approximate solutions with enhanced accuracy. Precisely, previous researches primarily concentrated on deriving approximate solutions via the first-order amplitude equations. However, this paper constructs approximate solutions by utilizing both first-order and second-order amplitude equations. And, we rigorously prove that such approximate solutions enjoy improved convergence property. To further illustrate our demonstration intuitively, we apply our main theorem to stochastic Allen–Cahn equation and present a numerical analysis. • The high-order amplitude equations of SPDEs with multiplicative noise is obtained. • The provision of approximate solutions with enhanced accuracy is given. • The approximate solutions enjoy improved convergence property is rigorously proved. • Applications and numerical analysis to stochastic Allen–Cahn equation are presented. [ABSTRACT FROM AUTHOR]

In this paper, an element-free Galerkin (EFG) method is developed for the numerical analysis of the time-fractional subdiffusion equation. By using the L 2 − 1 σ formula to approximate the Caputo fractional derivative, a second-order accurate scheme is proposed to achieve temporal discretization. Then, time-independent integer-order boundary value problems are formed, and a stabilized EFG method is applied to establish the discretize linear algebraic systems. Error of the proposed meshless method is proved theoretically. Numerical results show the convergence and effectiveness of the method. [ABSTRACT FROM AUTHOR]

The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1 / 2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others. We consider the case where the underlying process is a Brownian motion with drift. The price of a barrier option coincides with the price of a vanilla option of the "symmetrized" diffusion, which has a discontinuous drift. The symmetrized diffusion is then approximated by a Markov chain and the corresponding option price is calculated. This approximation to the barrier option is shown to have a convergence order of 1 under some mild condition on the initial value of the process and the payoff function. [ABSTRACT FROM AUTHOR]

This paper analyses the generalised collocation Trefftz method which allows to combine the advantages of the T -Trefftz and MFS. The initial idea of the method is to approximate the solution with a linear combination of many basis functions with many source points. The application of only one source point with nonsingular basis function allows for set up linearly independent set. On the other hand, using logarithmic and negative power bases for the source points enables better control over quality of the solution. The validity of the proposed method is conducted for the potential problem in a two-dimensional simply and doubly connected domain without using the domain decomposition. [ABSTRACT FROM AUTHOR]

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS 304) and low-carbon steel (AISI 1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the non-dimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter. [ABSTRACT FROM AUTHOR]

The goals of this paper are twofold: selection of pseudo-boundaries for sources nodes in the method of fundamental solutions (MFS), and comparisons of the MFS, the method of particular solutions (MPS) and the MFS-QR of Antunes. To pursue better pseudo-boundaries, we provide new estimates of the condition number (Cond) by the MFS for arbitrary pseudo-boundaries, and propose a new sensitivity index of stability via accuracy. Numerical experiments and comparisons are carried out to verify the analysis made. For five-pedal-flower-like domains, numerical comparisons are made by the sensitivity index. Circular pseudo-boundaries are optimal for highly smooth solutions, but the pseudo-boundaries near the domain boundary may be better for singular solutions. In this paper the gap has been shortened between theoretical analysis and numerical computation of the MFS, to provide some guidance for users. This is the first goal of this paper. The second goal is to compare the MFS, the MPS and the MFS-QR. Characteristics of the MFS-QR are explored. The new basis functions of the MFS-QR are the very particular solutions (PS), and the MFS-QR may be regarded as a special MPS. The MFS-QR is not a variant of the MFS but a variant of the MPS. The MFS-QR also plays a role in bridging from the MFS to the MPS. Both the MFS and the MPS can also be recognized as twins via the MFS-QR in the Trefftz family. The comparisons in this paper are more comprehensive. [ABSTRACT FROM AUTHOR]

As the backbone of social development, college students' level of physical exercise has always been the focus of research by experts and scholars. Most of the research methods are on the strength of literature data, questionnaire survey, mathematical statistics and comparative analysis. Based on the classification of college students and the influence and flow law of inter-class population, this paper establishes a differential equation system. By analyzing the existence and stability of the equilibrium of this system and the possible fold or backward bifurcations at the equilibrium, the quantitative analysis of college students' physical exercise trends on campus is carried out. This paper aims to improve the participation of college students in physical exercise by maximizing the number of students in the third categories. The results of theoretical proof, sensitivity analysis and numerical simulation show that in the initial stage, promoting peer-to-peer communication is the most effective measure. Secondly, when the effect of peer-to-peer interaction reaches saturation point, the way to improve physical education can achieve significant results. To fundamentally improve the enthusiasm of college students to participate in sports activities, we should start from the level of consciousness and enhance students' awareness of physical exercise from an early age. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIR model. For the real significance of the numerical analysis on stochastic SIR model, a linearly implicit Euler method with truncated Wiener process is introduced. The numerical positivity is obtained by the truncated Wiener process, which is the basis for the investigation of convergence and dynamical behavior. The numerical dynamical behavior is obtained by an exponential presentation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIR model. [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]

Artificial upwelling by the use of airlift pump is regarded as an effective way in utilizing deep ocean water and actualizing ocean fertilization. This paper focuses on numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system based on one-dimensional multi-fluid model. The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are calculated by solving the governing equations or by integrating the vector form of nonhomogeneous ordinary differential equation for two-phase flow interval. Upon successful verification of the present numerical model through a comparison with precedent theoretical and experimental results in case of a vertical pipe with length of 7.86 m, the model is extended to the case of artificial upwelling from water depth of 2000 m. The effects of submerged depth of air–water mixer on the pumped amount of water and the depth distributions of 6 physical quantities are considered. • This paper is concerned with numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system to lift deep ocean water. • The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are obtained from one-dimensional multi-fluid model. • The present model can be applied to predict the performance of airlift pump for lifting deep ocean water and the depth distributions of 6 physical quantities in axial direction. [ABSTRACT FROM AUTHOR]

As information continues to expand and uncertainty intensifies, traditional three-way decision methods in multi-criteria environments often appear inadequate when dealing with ranking problems. Most traditional three-way decision methods usually rely on subjective concepts or require decision-makers to specify probability parameters when constructing scheme descriptions, which leads to high subjectivity of the methods. Based on this background, this paper proposes an optimization-based three-way decision model for multi-criteria ranking strategy considering intuitionistic fuzzy concept, with the aim of mitigating the excessive subjectivity observed in most of the three-way decision methods. Firstly, a scheme-oriented intuitionistic fuzzy concept is defined to represent the decision-maker's fuzzy perception and selection of the scheme. Then, using the scheme-oriented intuitionistic fuzzy concept and the classic description of candidate schemes obtained through intuitionistic fuzzy c -means clustering algorithm, this paper provides a new method for estimating the conditional probability of the schemes that is not limited by parameter settings. Secondly, combining the scheme-oriented intuitionistic fuzzy concept and intuitionistic fuzzy information table, a new risk loss function is proposed, which is suitable for decision problems under intuitionistic fuzzy environment. Then, based on three-way decision model formulated using an optimization-based approach, an objective new ranking strategy is constructed. In addition, numerical analysis, comparative analysis, and parameter analysis are used to validate the rationality and feasibility of the presented ranking strategy. Finally, through quantitative analysis of multiple datasets and qualitative analysis of several ranking models, the operability of the new ranking strategy is verified. [ABSTRACT FROM AUTHOR]

The present paper performed a numerical study on two-phase nanofluid (NFs) flow in a circular heatsink for cooling several LEDs. The heatsink is symmetrically designed and has two inlets and four outlets. Six heat sources or LEDs are placed on the circumference of a circle and a heat source is also mounted in the center of the heatsink. By varying the diameter of the circle, the side length of the heat sources, and the input velocity of the NFs, one may estimate the values of thermal resistance (THR), temperature uniformity (TUY) on the heatsink, heat transfer coefficient (HTC), and pressure drop in the heatsink. The finite element and two-phase mixture method are utilized for NFs simulations. It demonstrate that the heat source placed in the middle has a lower temperature than other heat sources. The results are most significantly affected by changing the NFs' velocity. The value of dimensionless temperature increases and subsequently decreases as the sides of the heat sources get longer. The dimensionless temperature first decreases and then increases as the distance between the heat sources and the heatsink's center increases. The amount of THR is high when the heat sources' side length or velocity values are large. [ABSTRACT FROM AUTHOR]

In this paper, we focus on develop high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schrödinger equations. By constructing a new generating function, we obtain a fourth-order numerical differential formula and use it to approximate the spatial Riesz derivative, while the Crank–Nicolson method is applied for the time derivative. Based on the energy method, the conservation, solvability and convergence of the numerical algorithm are proved. Finally, some numerical examples are used to verify the correctness of the theoretical analysis and the validity of the numerical algorithm. [ABSTRACT FROM AUTHOR]

This study addresses the accuracy of stochastic simulations performed in Two-Dimensional Stochastic Neural Fields (2D-SNFs) with the infinite signal transmission speed and in the presence of external stimuli input. The numerical method in use belongs to the family of Galerkin-kind spectral approximations to Two-Dimensional Stochastic Neural Field Equations (2D-SNFEs). It translates the partial integro-differential fashion of such models into a large system of ordinary Stochastic Differential Equations (SDEs). Eventually, these SDEs are integrated approximately by the Euler–Maruyama scheme of the strong convergence order 0.5. In this paper, we devise a different-order approximate solution to the SNFE models at hand and look at the difference of such stochastic simulations on average for evaluating the consistency of the Euler–Maruyama-based numerical solution derived. The error committed in the 2D-SNFE-numerical-integration-scheme under study becomes available in our research. The other issue of particular attention and interest is hidden state reconstructions rooted in the 2D-SNFE approximations and incomplete noisy measurements of the membrane potential fulfilled at some user-assigned space positions and time instants. This statement leads to high-dimensional prediction and filtering problems to be solved. Here, we implement the Extended Kalman Filtering (EKF) approach, but accommodate it to our 2D-SNFE-oriented data assimilation scheme of huge size because of the two-dimensional manner of the stochastic process models in use. A sound performance of the newly-devised hidden state estimation technique is observed and exposed on a challenging 2D-SNFE example of computational neuroscience in Matlab. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a meshless method for numerical simulation of nonlinear Klein–Gordon equations. The method begins with a temporal discretization to address time derivatives. The stability and error of the temporal discretization scheme are theoretically analyzed. Subsequently, meshless algebraic systems of Klein–Gordon solitons are established by using the superconvergent finite point method (SFPM) for spatial discretization. The moving least squares approximation and its smoothed derivatives are adopted in the SFPM to ensure the high accuracy and remarkable superconvergence. Accuracy and convergence of the meshless numerical simulation for nonlinear Klein–Gordon equations are analyzed in theory. Numerical results validate the superconvergence and effectiveness of the method and confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Observational studies often rely on sample survey data for estimation, given the difficulty of obtaining exhaustive information for the entire population. However, the use of sample data can lead to a reduction in estimation efficiency due to sampling error. When certain population-level data are accessible, devising an effective strategy to integrate them into the underlying estimation process proves advantageous. This paper proposes a methodology based on empirical likelihood for conducting quantile regression analysis on longitudinal data while incorporating population-level information. Both theoretical analysis and numerical simulations demonstrate that the proposed approach outperforms estimation methods that do not leverage population-level data. [ABSTRACT FROM AUTHOR]

Firing activities provide the potential possibility for achieving bio-brain functionality with high energy-efficient and high-speed information processing performance. This inspires the design of bionic circuits to generate firing activities and develop brain-like applications. In this paper, a dual mem-elements based cellular neural network (CNN) cell is constructed to produce bionic firing activities, in which a non-ideal memcapacitor and an N-type locally active memristor are employed to emulate the functions of the neuronal membrane. The proposed CNN cell has an excitation-dependent equilibrium trajectory and stability. Numerical analysis shows that the dual mem-elements based CNN cell has abundant dynamical behaviors of forward/reverse period-doubling bifurcation routes, chaos crisis, tangent bifurcation, and bubbles with the change of model parameters of the CNN cell, memcapacitor, and exciting source. As a result, the rich firing patterns' transition can be observed from the two-dimensional dynamics evolution. The analog circuit of the proposed CNN cell is designed, and then a PCB-based hardware circuit is implemented. The experimental results certify the accuracy of the theoretical and numerical analysis. • A dual mem-elements based CNN cell is newly proposed by employing memristor and memcapacitor. • Bionic firing activities of the periodic/chaotic spiking behaviors are numerically disclosed. • Mem-element emulators based CNN circuit is manually made and hardware experiments are executed. [ABSTRACT FROM AUTHOR]

The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed. • Interface analysis of magnetic fluids by the Boundary Element Method. • Magnetic and fluid potentials and normal derivatives on arbitrary-shaped interface. • Multi-valued quantities at points where boundaries cross sharply are allowed. • Uniform vector field conditions avoid the singularity in fundamental solution. • A code generates magnetic field and fluid velocity on interface as intended. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a thermal frictional contact model with damage and long memory effects. We consider a deformable body made of viscoelastic material and assume the process to be dynamic. The material is expected to adhere to the Kelvin–Voigt constitutive law, with damage and thermal effects incorporated. The variational formulation of the model results in a coupled system comprising a history-dependent hemivariational inequality governing the displacement field, a parabolic variational inequality describing the damage field and an evolution equation for the temperature field. In the analysis of this system, we initially introduce a fully discrete scheme, and then concentrate on deriving error estimates of numerical solutions. An optimal order error estimate is attained under some appropriate solution regularity assumptions. At the tail of this manuscript, numerical simulations are provided for the contact problem to validate the theoretical results. • We have studied a complex thermoviscoelastic contact model with damage and long memory. • The variational formulation gives rise to a differential hemivariational inequality. • We focus on optimal error estimates of numerical solutions. • Theoretical analysis and numerical simulation have faced considerable challenges. [ABSTRACT FROM AUTHOR]

• The simulation and numerical analysis of EM materials are reviewed, from numerical analysis of dielectric parameters, simulation of wave absorbing performance, electromagnetic performance improvement, and structural construction optimization. • For the EM response mechanism, radiation-dependent relaxation and charge transport energy transitions are dissected. • For the EM calculation section, two leading roles are highlighted, including the purposeful design of EM and the provision of theoretical guidance for optimizing electromagnetic absorption performance. • In addition, this paper points out the current problems and potential opportunities in the numerical simulation of absorbing materials, point out the new development direction and proposes prospects. Electromagnetic absorbers (EMA) have driven the development of Electromagnetic (EM) technology and advanced EM devices. Utilizing the EM energy conversion of EM absorbers to design various devices is attractive and promising, especially in personal protection and healthcare. In this review article, the simulation and numerical analysis of EM materials are reviewed, from numerical analysis of dielectric parameters, simulation of wave absorbing performance, electromagnetic performance improvement, and structural construction optimization. For the EM response mechanism, radiation-dependent relaxation and charge transport energy transitions are dissected. For the EM calculation section, two leading roles are highlighted, including the purposeful design of EM and the provision of theoretical guidance for optimizing electromagnetic absorption performance. In addition, this work points out the current problems and potential opportunities in the numerical simulation of absorbing materials, points out the new development direction, and proposes prospects. [Display omitted]. [ABSTRACT FROM AUTHOR]

In this paper, the Tsallis entropy based novel uncertainty relations on vector signals and matrix signals in terms of sparse representation are deduced for the first time. These new uncertainty bounds are not only related with the entropy parameter, but also related with the vector length, the min non-zero correlation between standard orthogonal basis and the given signals, the max correlation between the two given orthogonal basis and even the eigenvalues along with eigenvectors. Especially, the relationship between uncertainty bounds and matrix eigenvalues is discussed as well, as discloses the new interesting interpretation on sparse representation. In addition, the theoretical analysis and numerical examples have been shown to verify these newly proposed uncertainty principles, e.g., under the case of special parameters of Tsallis entropy, the uncertainty bound reaches its peak value for the sparsest representation of matrix (i.e., only one eigenvalue is not zero). Moreover, various numerical relations between uncertainty bounds and Tsallis entropy parameters are shown in perceptual form, as maybe give us the possible enlightenment or guidance in future sparse representation analysis. [ABSTRACT FROM AUTHOR]

This paper is devoted to develop a truly meshless numerical procedure for the fully non-linear analysis of sloshing phenomenon in an arbitrary-shape tank. For this purpose, the potential theory is considered as a liquid sloshing model, and the Lagrangian form of kinematic and dynamic boundary conditions in a moving coordinate system fixed to the tank is used to accurately capture the free surface. The multi-quadric radial basis function (MQ-RBF) augmented with the polynomial terms is employed to determine RBF-FD weights on neighboring nodes surrounding the center point for the spatial derivatives. These weight coefficients are used to solve both boundary value problems for velocity and acceleration potential. Compared with mash-based methods, the present method has the advantage of being easy to construct and flexible in dealing with the moving boundary problems. The free surface elevations, hydrodynamic pressure, and first-order natural sloshing frequencies have been reported for various geometries tanks under horizontal excitations at resonance and non-resonance cases. Fairly satisfactory agreement is observed in the numerical results and exiting results, especially for free surface elevation and first-order natural sloshing frequency. [ABSTRACT FROM AUTHOR]

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied. [ABSTRACT FROM AUTHOR]

This paper deals with the H ∞ state estimation problem for a class of networked multi-rate time-varying systems with estimation error variance constraint. The redundant channel transmission scheme is employed to reduce the packet dropout rate and improve the quality of the data delivery. By utilizing the lifting technique, an augmented estimation error system is established with a uniform sampling rate. The objective of this paper is to design a time-varying state estimator such that, in the simultaneous presence of the asynchronous sampling, probabilistic packet dropouts as well as stochastic noises, the error dynamics of the state estimation satisfies both the prescribed H ∞ performance requirement and the prescribed estimation error variance constraints. Through intensive stochastic analysis, sufficient conditions are established to ensure the existence of the desired estimator whose parameters are determined by solving a set of recursive linear matrix inequalities. A numerical example is presented to show the validity of the proposed estimation strategy. [ABSTRACT FROM AUTHOR]

• Fractional-order models are more accurate than integer-order models in reflecting some properties of objects when studying practical problems. • This paper analyses the relationship between enterprise management and financial performance, mathematically models its relationship. • We constructs fractional differential equations, and tests it through empirical research. • The influence of the characteristics of management age, international experience, team size etc. on the financial performance of the company. With the development of science and technology, people also find that fractional-order models are more accurate than integer-order models in describing some phenomena and reflecting some properties of objects when studying practical problems. Since the fractional derivative is a quasi-differential operator, its memory-preserving non-locality, while beautifully portraying the real problem, also brings considerable difficulties to theoretical analysis and numerical calculation. This paper analyses the relationship between enterprise management and financial performance, analyses the mean and heterogeneity of the characteristics of enterprise management team, mathematically models its relationship, constructs fractional differential equations, and tests it through empirical research. The influence of the characteristics of enterprise management age, international experience, education level, team size and government background on the financial performance of the company. [ABSTRACT FROM AUTHOR]

• Sufficient conditions are established for a singular Cucker–Smale model with a general target motion pattern driving force to admit an asymptotic flocking. • A critical value of the exponent in the communication weight is given to lead to global regularity of solutions. • The avoiding collision asymptotic flocking of Cucker–Smale model with a general target motion pattern driving force is obtained for the first time in the literature. • It is the first time to show that the particles finally come to a line-shape formation with collision avoiding by theoretical proof in this paper. This paper is concerned with a singular Cucker–Smale model with a general targeted pattern driving force, which ensures that the particles finally come to the desired spatial configuration. Under some suitable conditions, we prove that the exponent α ≥ 1 in the communication weight leads to global regularity of solutions so that the system has an asymptotic flocking without collision between any agent. As an example, a prescribed driving force is given to demonstrate that the particles finally come to a line-shaped formation with collision avoidance, which can be viewed as a reasonable explanation for the wild geese flying in a line-shape in the sky. Moreover, this mechanism can be applied to the UAVs forming a line-shape to complete some special military missions. These results are novel, which are illustrated by both theoretical analysis and numerical simulations. [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]

Highlights • A period-dependent mathematical program with equilibrium constraints (PMPEC) is presented. • A two-stage model is presented. • A new solution method is proposed. • Numerical experiments are conducted and comparisons are made with existing signal controls. Abstract For a road networked system with stochastic travel demand, a two-stage model is proposed for period-dependent area traffic signal control. In this paper, a period-dependent mathematical program with equilibrium constraints (PMPEC) is presented to minimize total travel delay over successive time periods. For stochastic travel demand over multiple time periods, a period-dependent user equilibrium traffic assignment can be formulated as a variational inequality. Due to non-linearity of equilibrium constraints, a two-stage model is presented in this paper. In order to understand feasibility of the proposed model, numerical experiments using a real-data road network are conducted. The results indicate that the proposed model attains a promising system performance and exhibit computational advantage over existing alternatives. [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]