The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Cr...The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of θ（k2 ＋ h2）. Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.展开更多
In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponentia...In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of sin- gle solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.展开更多
We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration an...We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been conducted to demonstrate the accuracy of the current algorithm with relatively minimal computational effort. The results showed that use of the present approach in the simulation is very applicable for the solution of convection-diffusion equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithm is seen to be very good alternatives to existing approaches for such physical applications.展开更多
Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal expo...Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.展开更多
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep...In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.展开更多
Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it ...Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.展开更多
This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter...This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.展开更多
Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under satura...Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.展开更多
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof ar...In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .展开更多
By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε...By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.展开更多
The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varyin...The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.展开更多
A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an ...This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.展开更多
This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its...This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its control boundary.This research employs an advanced active disturbance rejection control framework,incorporating an innovative observer with adaptive gain characteristics for precise disturbance estimation,coupled with a robust feedback control mechanism for disturbance compensation.The theoretical analysis establishes rigorous convergence proofs for the proposed time-dependent extended state observer.Furthermore,this investigation utilizes semigroup theory to validate the closed-loop system’s well-posed.Through comprehensive Lyapunov-based analysis,this study confirms the system’s capability to achieve exponential convergence of tracking errors while effectively mitigating disturbance effects.Extensive numerical experiments corroborate the theoretical findings,demonstrating the control scheme’s practical efficacy.展开更多
The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic sol...The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,...This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.展开更多
Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(i...Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(ij )from v_(i)to v_(j)is defined as dij=P∈P(v_(i),v_(j))min∑w(e) where P(v_(i),v_(j)) denotes the set consisting of all the directed paths from v_(i)to v_(j)in G.Given a nonzero indeterminant q,following the definitions from Yan and Yeh (Adv.Appl.Math.,2007),and Bapat et al.(Linear Algebra Appl.,2006),one can define the exponential distance matrix of G as F^(q)_(G)=(q^(dij))_(n×n),and define the q-distance matrix of G as D_(G)^(q)=(d_(ij)^(q))_(n×n)with d_(ij)^(q)={1-q^(dij)/1-q,if q≠1,dij,if q=1,extending the original definitions only for the undirected unweighted connected graphs.One of the remarkable results about the distance matrices of graphs is due to the Graham-HoffmanHosoya theorem (J.Graph Theory,1977).In this paper,we present some Graham-HoffmanHosoya type theorems for the exponential distance matrix F_(G)^(q)and q-distance matrix D_(G)^(q),extending all the known Graham-Hoffman-Hosoya type theorems.展开更多
We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significa...We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.展开更多
We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave pr...We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.展开更多
文摘The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of θ（k2 ＋ h2）. Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.
基金supported by the Scientific and Technological Research Council of Turkey(Grant No.113F394)
文摘In this paper, an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions. Regularized long wave equation （RLW） is integrated fully by using an exponential B-spline Galerkin method in space together with Crank-Nicolson method in time. Three numerical examples related to propagation of sin- gle solitary wave, interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.
文摘We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been conducted to demonstrate the accuracy of the current algorithm with relatively minimal computational effort. The results showed that use of the present approach in the simulation is very applicable for the solution of convection-diffusion equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithm is seen to be very good alternatives to existing approaches for such physical applications.
文摘Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。
文摘In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.
文摘Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.
基金supported by the Na⁃tional Key R&D Program of China(No.2022YFC2204800)the Graduate Student Independent Exploration and Innovation Program of Central South University(No.2024ZZTS 0767).
文摘This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.
基金supported by the National Natural Science Foundation of China(62173215)the Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04,ZR2020ZD24)
文摘Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.
基金supported by the NSFC(12271141)supported by the Fundamental Research Funds for the Central Universities(B240205026)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX24_0821).
文摘In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .
基金supported by National Natural Science Foundation of China(No.12171152)。
文摘By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.
基金Supported by the National Natural Science Foundation of China(No.U22A20246)the Key Project of Natural Science Foundation of Hebei Province of China(Basic Research Base Project)(No.A2023210064)the Science and Technology Program of Hebei Province of China(Nos.246Z1904G and 225676162GH)。
文摘The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
文摘This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.
文摘This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its control boundary.This research employs an advanced active disturbance rejection control framework,incorporating an innovative observer with adaptive gain characteristics for precise disturbance estimation,coupled with a robust feedback control mechanism for disturbance compensation.The theoretical analysis establishes rigorous convergence proofs for the proposed time-dependent extended state observer.Furthermore,this investigation utilizes semigroup theory to validate the closed-loop system’s well-posed.Through comprehensive Lyapunov-based analysis,this study confirms the system’s capability to achieve exponential convergence of tracking errors while effectively mitigating disturbance effects.Extensive numerical experiments corroborate the theoretical findings,demonstrating the control scheme’s practical efficacy.
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.
文摘Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(ij )from v_(i)to v_(j)is defined as dij=P∈P(v_(i),v_(j))min∑w(e) where P(v_(i),v_(j)) denotes the set consisting of all the directed paths from v_(i)to v_(j)in G.Given a nonzero indeterminant q,following the definitions from Yan and Yeh (Adv.Appl.Math.,2007),and Bapat et al.(Linear Algebra Appl.,2006),one can define the exponential distance matrix of G as F^(q)_(G)=(q^(dij))_(n×n),and define the q-distance matrix of G as D_(G)^(q)=(d_(ij)^(q))_(n×n)with d_(ij)^(q)={1-q^(dij)/1-q,if q≠1,dij,if q=1,extending the original definitions only for the undirected unweighted connected graphs.One of the remarkable results about the distance matrices of graphs is due to the Graham-HoffmanHosoya theorem (J.Graph Theory,1977).In this paper,we present some Graham-HoffmanHosoya type theorems for the exponential distance matrix F_(G)^(q)and q-distance matrix D_(G)^(q),extending all the known Graham-Hoffman-Hosoya type theorems.
基金supported by the National Natural Science Foundation of China(Grant No.12174147)the Chinese Scholarship Council(Grant Nos.202108210152 and 202006175016).
文摘We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.
基金part supported by the NSF Grants DMS-1912654 and DMS 2205590。
文摘We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.
