In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.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
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 study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.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
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
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
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
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
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 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
In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to...In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to convert the nD CDE into a diffusion equation.Then,the converted diffusion equation is solved by the LB model.So,compared to the available LB models for CDE,the present LB model can eliminate the difficulty in treating the convection term.With the direct Taylor expansion method,it is shown that the CDE can be exactly derived from the exponential transformation based LB model.Finally,a variety of numerical tests have been conducted to validate the present LB model.It can be found that the numerical results agree well with the analytical solutions.Moreover,we also find that the present LB model has second-order convergence rate in space,and it is more effective and more stable than the previous LB model for the CDE.展开更多
In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by ...In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.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
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
A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the mode...A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the model parameters was also conducted. In the end, the superiority of the new distribution over the exponentiated exponential was made by means of data set.展开更多
The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and th...The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.展开更多
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
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.
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 and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
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.
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 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.
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 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) .
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 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.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.12072127 and 11702259)the Guidance Project of Scientific Research Program of Hubei Provincial Department of Education(Grant No.B2021322).
文摘In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to convert the nD CDE into a diffusion equation.Then,the converted diffusion equation is solved by the LB model.So,compared to the available LB models for CDE,the present LB model can eliminate the difficulty in treating the convection term.With the direct Taylor expansion method,it is shown that the CDE can be exactly derived from the exponential transformation based LB model.Finally,a variety of numerical tests have been conducted to validate the present LB model.It can be found that the numerical results agree well with the analytical solutions.Moreover,we also find that the present LB model has second-order convergence rate in space,and it is more effective and more stable than the previous LB model for the CDE.
文摘In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.
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.
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.
文摘A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the model parameters was also conducted. In the end, the superiority of the new distribution over the exponentiated exponential was made by means of data set.
基金The National Natural Science Foundation of China (No60574006)
文摘The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
