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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, 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]

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]

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]

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]

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]

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 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 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]

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]

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]

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]

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 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]

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]

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 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]

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 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]

The present paper is devoted to the study of a class of nonlinear Helmholtz equations that is essentially used in mathematical models for the theoretical and numerical analysis of scattering and radiation effects. While well-known works relate to geometrically simple domains (supporting the nonlinearity) and selected nonlinearities, the new aspects lie in the transition to more generally shaped, two- or three-dimensional objects, to more general nonlinearities (including saturation), and in the possibility of an efficient numerical approximation of the electromagnetic fields and derived quantities (such as energy, transmission coefficient, etc.). The paper describes and investigates an approach that consists in transforming the original full-space transmission problem for a nonlinear Helmholtz equation into an equivalent boundary-value problem on a bounded domain by means of a nonlocal Dirichlet-to-Neumann (DtN) operator. It is shown that the transformed nonlinear problem is equivalent to the original one and is uniquely solvable under appropriate conditions. In addition, the effect of truncation of the DtN operator on the resulting solution is investigated. It is shown that the corresponding sesquilinear form satisfies a parameter-uniform inf–sup condition, that the modified nonlinear problem has a unique solution, and that the solution error caused by the truncated DtN operator can be estimated in dependence on the truncation parameter. • The response of a penetrable obstacle under an electromagnetic field is considered. • The constitutive law of the obstacle is nonlinear. • The mathematical model is a transmission problem for a nonlinear Helmholtz equation. • Existence, uniqueness of the solution of a spatially reduced problem are proved. • A parameter-independent stability estimate and an error estimate are given. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic delay model for a mechanical centrifugal governor system with noise. The Hopf bifurcation of the system is obtained with the delay as a parameter. Considering the effect of delay, the stochastic bifurcation of the system is obtained, as well as the stochastic bifurcation diagrams of the model by numerical analysis. It is found that large delays can lead to the occurrence of stochastic bifurcations, which destabilize the system. Moreover, retaining the quadratic term of ϵ induces a new dynamical phenomenon - stochastic P-bifurcation. When spectral density is used as a bifurcation parameter, the periodicity of the system is influenced. The results of this paper are a reference value for preventing instability in mechanical systems. Meanwhile, the theoretical work and numerical simulations in this paper can be extended to other systems. [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, 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]

• 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]

• 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]

Given the uniform structure observed in existing conservative chaotic systems, this paper presents a novel approach for constructing 3D conservative chaotic systems with dissipative terms, utilizing the Shilnikov theorem. To demonstrate the effectiveness of the proposed method, an example system is presented. The researches show that the dissipative term and angular frequency have important influence on the motion of system. Remarkably, this system exhibits distinct forms of conservative chaos and invariant torus. Additionally, we further propose a derivative system of the example system to expand its range of motion. Numerical analysis reveals an intriguing coexistence phenomenon in the system, which will be visually demonstrated using phase diagrams and basins of attraction in the paper. Finally, the analog circuits for both systems are designed, yielding results that closely matched the numerical simulations. • Based on Shilnikov theorem, we propose a method to construct 3D autonomous conservative system with dissipative term. • An example system is presented and its conservative dynamics are investigated in depth. • The derivative system of the example system is proposed. • An analog circuit in PSpice is designed. [ABSTRACT FROM AUTHOR]

This paper is focused on the application of higher order meshless schemes in a numerical analysis of selected thermomechanical problems. Numerical investigation is based upon meshless Finite Difference method as well as its combinations with Finite Element method, performed at two different levels of analysis. The first variant assumes conjugation of element and meshless approximation schemes, while in the second one, the problem domain is divided into several disjoint subdomains, with a parallel and independent operating of coupled methods in each subdomain. The most important advantage of the applied approximation technique is no requirements of modification or enhancement of the existing discretization model. Therefore, high approximation orders may be assumed without providing new nodes, elements and degrees of freedom, maintaining the entire numerical model as simple as possible. This approach is especially convenient in coupled multi-field 2D and 3D problems, for instance stationary and non-stationary thermoelastic ones. In those problems, standard higher order approximation techniques may lead to complex numerical models caused by the rapid growth of a number of degrees of freedom and ill-conditioned schemes. The proposed approach is derived for three dimensional non-stationary thermoelastic problems. Moreover, it is examined on variety of 2D and 3D benchmark examples and engineering applications. Both solution accuracy and convergence rate are taken into account. Obtained results are very promising as they reflect the competitiveness of the approach comparing to other commonly applied higher order approaches. [ABSTRACT FROM AUTHOR]

Despite the widespread use of transcendental functions in the modeling of the dynamics of DNA, most research efforts are limited in their analytical studies of this enthralling system to cubic order polynomial approximations of the corresponding equations of motion. In this paper, we present an investigation of waves in the Peyrard–Bishop–Dauxois model of DNA; while extending the polynomial approximation of the Morse potential up to the sixth order. We show that, within a generalized version of the reductive perturbation method that we have adopted, the equations governing the envelop consist of the standard cubic nonlinear Schrödinger equation and its non homogeneous linearizations. Exact and explicit analytical solutions that correspond to bright solitary waves are obtained for these coupled amplitude equations. A notable qualitative feature of these solutions is the dependence of their propagation speeds and frequencies on their amplitudes. Our approach additionally unveils that these solutions contain some harmonic terms; which are missed in existing works. A very good agreement is found between our analytical analysis and the numerical simulations of the full discrete nonlinear equation of the lattice which use these solutions as initial conditions. • Peyrard–Bishop–Dauxois model of DNA expanded up to fifth order of perturbation. • A generalized reductive perturbation method is employed for the derivations. • The envelop is described by coupled nonlinear and linear Schrodinger equations. • Exact analytical solutions are derived. • Higher order corrections to wave's speed and pulsations, are established. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative properties of the fixed points in the non-hyperbolic cases, codimension-one bifurcations and weak resonances of a Cournot-Bertrand duopoly mixed competition model are explored. The two firms adopt different decision variables and different objective functions, which are more consistent with the actual economic market situation. The qualitative properties of all the fixed points in the non-hyperbolic cases are investigated using the reduction principle and the center manifold theorem. After that, all the potential codimension-one bifurcations, including transcritical bifurcation, supercritical or subcritical flip bifurcation and Neimark–Sacker bifurcation are analyzed using the bifurcation theory and the center manifold theorem. The direction, stability, and even the explicit approximate expression are derived for each type of bifurcation. By perturbing the closed invariant curve caused by the Neimark–Sacker bifurcation, the 2 : 5 weak resonance associated with Arnold's tongue is theoretically proved, and the absence of 1 : 6 and 5 : 6 weak resonances is further analyzed. A large number of numerical simulations show complete consistency with all theoretical analyses. Moreover, the continuation method is used to conduct numerical bifurcation analyses, further verifying the correctness of theoretical analyses, and testing more codimension 2 bifurcations, such as fold-flip bifurcation, generalized flip bifurcation and 1 : 2 strong resonance. In addition, the economic implications of these bifurcations are also explained accordingly. [ABSTRACT FROM AUTHOR]

• A model of a nonlinear magnetic coupling with a piezoelectric vibration energy harvester is developed, incorporating dimensions. • Numerical solutions of nonlinear energy harvesting systems are studied by using the Runge-Kutta method. • Nonlinear characteristics of the model were investigated at different constant frequencies. • The numerical and theoretical solutions are verified under up and down sweep with performing in output voltage response. • Experimental validation is conducted to measure the nonlinear restoring force and examine the performance of nonlinear bistable and monostable energy harvesters. Vibration based piezoelectric energy harvesting has been receiving more and more attention for supplying usable electrical energy to low-power electronic devices. This type of energy can produce the desired voltage to power any low electronic device or wireless sensor. But most of them provide lower voltage and insufficient power. In this paper, the nonlinear magnetic field is introduced to broaden the effective resonant bandwidth for overcoming this issue. The dynamic linear and nonlinear model of magnetic coupling piezoelectric vibration energy harvester is established based on the Hamilton principle, Euler-Bernoulli beam theory, piezoelectric theory, and Kirchhoff's law and law of mechanics. Numerical solutions of nonlinear energy harvesting systems are studied by using the Runge-Kutta method. The bifurcation diagram, Poincare map, power spectrum, and phase trajectory of voltage output are investigated with different excitation amplitudes and frequencies. Simulation of linear and nonlinear model were illustrated at given excitation levels. Simulation results show the harvesting performance can be improved by proper external magnetic coupling and potential energy function. The theoretical harmonic balance analysis results verify the numerical solution and influence the mechanism of excitation levels and interface resistances. Experimental verification is carried out to measure the nonlinear restoring force and examine the performance of nonlinear bistable and monostable energy harvesters. The experiment results show the nonlinear bistable and monostable energy harvesters can provide larger voltage and more power. [ABSTRACT FROM AUTHOR]

In this paper, the memory property and the historical dynamic information of a fractional system via event-triggered control are studied. A unit step function is introduced and the control input is taken as a piecewise function. By theorem analysis and numerical simulations, it is shown that the fractional calculus of a piecewise function is relevant to the entire historical dynamic information and cannot be calculated in segments because of its memory property. So, the state of a fractional system via event-triggered control is affected by all input from the initial time, but not the triggering time, to the current time. But in previous studies, this property is neglected and the historical dynamic information has not been fully studied, which disagrees with the real physical systems. Therefore, the historical dynamic information of a fractional system via event-triggered control should be studied in order to satisfy the demands in engineering. [ABSTRACT FROM AUTHOR]

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance "1" can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets. [ABSTRACT FROM AUTHOR]

Sometimes a robustness analysis of a linear discrete system (LDS) implies a study of stability in view of parametric variations in a set A. This leads to a stability analysis of a family of polynomials (FOP) denoted by F A. Some of these families are the well-known family of interval polynomials (FOIP) denoted by F B n , where B n is an (n + 1) -dimensional box , and the one-parameter family of polynomials denoted by F C n , where C n is an (n + 1) -dimensional curve. Currently, there are several results to ensure the stability of these families. However, they are usually laborious processes, especially if the dimension of A is large and unfortunately for LDS there is not an analogous result to Kharitonov's Theorem for linear continuous systems (LCS). This paper proposes necessary and sufficient conditions to determine Schur stability of F A. We prove the existence of an extreme point α ∗ ∈ A such that the stability of the corresponding extremal polynomial f (α ∗ , x) determines the stability of the entire family F A , where A is a compact set. It is also shown that α ∗ cannot be an interior point of A , so that α ∗ ∈ ∂ A. For some F B n and F C n , it is obtained an extremal polynomial or simple inequalities. This analysis and numerical examples suggest that the conditions proposed are a prominent alternative to results found in the literature. • An extremal polynomial f (α ∗ , x) determines stability of a family F A , A compact, α ∗ ∈ ∂ A. • Criteria for stability of F A , A = B n , C n (box, and curve), are proposed. • Numerical examples illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the rigorous derivation of some discrete versions of stochastic Grönwall inequalities involving a martingale, which are commonly used in the numerical analysis of multi-term stochastic time-fractional diffusion equations. A Grönwall lemma is also established to deal with the numerical analysis of multi-term stochastic fractional diffusion equations with delay. The proofs of the established inequalities are based on a corresponding deterministic version of the discrete fractional Grönwall lemma in case of smooth solutions and an inequality bounding the supremum in terms of the infimum for discrete time martingales. A numerical application is introduced finally in which the constructed inequalities are handled to derive a priori estimates for a discrete fractional stochastic model. [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]

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 To efficiently analyze electromagnetic scattering of electrically-large complex objects, a novel version of multilevel directional simply sparse method (MLDSSM) based on well-conditioned electric field integral equation (WEFIE) is proposed in this paper. When the complex target is analyzed, the condition number of impedance matrix of electric field integral equation (EFIE) is very poor. In this paper, the WEFIE is applied to improve the convergence property of EFIE. Meanwhile, an efficient version of MLSSM algorithm based on directional grouping scheme is applied to further accelerate the matrix-vector multiplication. Numerical results of differently shaped objects were presented to show the efficiency of the proposed method. [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]