In this paper,we consider the plasma-vacuum interface problem in a cylindrical tube region impressed by a special background magnetic field.The interior region is occupied with plasma,which is governed by the incompre...In this paper,we consider the plasma-vacuum interface problem in a cylindrical tube region impressed by a special background magnetic field.The interior region is occupied with plasma,which is governed by the incompressible inviscid and resistive MHD system without damping term.The exterior vacuum region is governed by the so-called the“pre-Maxwell equations”.And on the free interface,additionally,the effect of surface tension is taken into account.The original region can be transformed into a horizontally periodic slab through the cylindrical coordinate transformation,which will be impressed by a uniform nonhorizontal magnetic field.Appending with the appropriate physical boundary conditions,the global well-posedness of the problem is established by the energy method.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
Guangxi Province is a large agricultural province and agricultural eco-environment protection becomes important. The research analyzed major problems of agricultural eco-environment and proposed a series of countermea...Guangxi Province is a large agricultural province and agricultural eco-environment protection becomes important. The research analyzed major problems of agricultural eco-environment and proposed a series of countermeasures to improve Guangxi agricultural eco-environment and provides references for agricultural eco-environment protection in Guangxi and agricultural development.展开更多
A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value prob...A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.展开更多
This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier tec...This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems ar...The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.展开更多
On the basis of introducing and defining the concept of rural land circulation,this paper discussed the inevitability of rural land circulation in China and analyzed the main problems in the rural land circulation. Fi...On the basis of introducing and defining the concept of rural land circulation,this paper discussed the inevitability of rural land circulation in China and analyzed the main problems in the rural land circulation. Finally,it came up with some pertinent recommendations for the government in the rural land circulation in China,including formulating the relevant administrative rules and regulations,improving the rural land circulation policy system,improving the rural social security system and relieving the worry of farmers in land circulation,energetically promoting institutional construction,and actively cultivating rural land circulation market.展开更多
An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume...An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.展开更多
The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (...The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.展开更多
The mechanisms of the February 3, 1996 Lijiang main shock, Yunnan Province, are estimated by using the principle to inverse the mechanisms of two point sources simultaneously. The results are that the main shock of Li...The mechanisms of the February 3, 1996 Lijiang main shock, Yunnan Province, are estimated by using the principle to inverse the mechanisms of two point sources simultaneously. The results are that the main shock of Lijiang consists of two large ruptures, the time difference and the distance between the two ruptures are about 12 s (by the inversion) and about 26 km respectively. An extensional normal with strike-slip fault in about the north-south direction was formed by the first rupture, the mechanism of the second rupture is to be further studied. The method to inverse mechanisms of two point sources at the same time and the results obtained by directly analyzing P waveform records of the main shock are introduced, some related problems are also discussed. The Wuding earthquakes of October, 1995 and the Lijiang earthquake are considered to be the manifestation of the same dynamic process at different temporal and spatial points and the occurrence order of the two earthquakes is related to the direction of dynamics transmission.展开更多
In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component i...In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.展开更多
To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainabili...To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when ...In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.展开更多
Denote by M the 'second main term' attached to the Siegel zeros of Dirichlet L-functions in odd Goldbach problem. Let N≥exp(exp(9.873)) be a real number, r=logN, the statement M≤0.032 N^2r^(-3) is proved in ...Denote by M the 'second main term' attached to the Siegel zeros of Dirichlet L-functions in odd Goldbach problem. Let N≥exp(exp(9.873)) be a real number, r=logN, the statement M≤0.032 N^2r^(-3) is proved in this paper.展开更多
In this paper,the boundary knot method is applied to simulate inverse problems of determining physical boundary occurring in an inaccessible interior part.This is fulfilled from measurements of the partially accessibl...In this paper,the boundary knot method is applied to simulate inverse problems of determining physical boundary occurring in an inaccessible interior part.This is fulfilled from measurements of the partially accessible outer boundary.The truncated singular value decomposition under parameter choice of the cross validation method is employed for noisy boundary data cases.Numerical results for two benchmark problems show that the boundary knot method is simple,accurate,stable and computationally efficient for inverse problems under domains with doubly connected domains.展开更多
In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve t...In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.展开更多
基金supported by the NSFC(11571177)the National Key Research and Development Program of China(2020YFA0713803).
文摘In this paper,we consider the plasma-vacuum interface problem in a cylindrical tube region impressed by a special background magnetic field.The interior region is occupied with plasma,which is governed by the incompressible inviscid and resistive MHD system without damping term.The exterior vacuum region is governed by the so-called the“pre-Maxwell equations”.And on the free interface,additionally,the effect of surface tension is taken into account.The original region can be transformed into a horizontally periodic slab through the cylindrical coordinate transformation,which will be impressed by a uniform nonhorizontal magnetic field.Appending with the appropriate physical boundary conditions,the global well-posedness of the problem is established by the energy method.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金Supported by Guangxi Natural Science Foundation(0708226)Guangxi Distinguished Experts Special Fund~~
文摘Guangxi Province is a large agricultural province and agricultural eco-environment protection becomes important. The research analyzed major problems of agricultural eco-environment and proposed a series of countermeasures to improve Guangxi agricultural eco-environment and provides references for agricultural eco-environment protection in Guangxi and agricultural development.
文摘A class of nonlocal boundary value probl em s for elliptic systems in the unbounded domains are considered. Under suitable c onditions, the existence of solution and the comparison theorem for the boundary value problems are studied.
文摘This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金The project supported by the National Natural Science Foundation of China
文摘The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied.
文摘On the basis of introducing and defining the concept of rural land circulation,this paper discussed the inevitability of rural land circulation in China and analyzed the main problems in the rural land circulation. Finally,it came up with some pertinent recommendations for the government in the rural land circulation in China,including formulating the relevant administrative rules and regulations,improving the rural land circulation policy system,improving the rural social security system and relieving the worry of farmers in land circulation,energetically promoting institutional construction,and actively cultivating rural land circulation market.
基金Financial support for the project from the National Natural Science Foundation of China(No.51609181)
文摘An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.
文摘The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.
文摘The mechanisms of the February 3, 1996 Lijiang main shock, Yunnan Province, are estimated by using the principle to inverse the mechanisms of two point sources simultaneously. The results are that the main shock of Lijiang consists of two large ruptures, the time difference and the distance between the two ruptures are about 12 s (by the inversion) and about 26 km respectively. An extensional normal with strike-slip fault in about the north-south direction was formed by the first rupture, the mechanism of the second rupture is to be further studied. The method to inverse mechanisms of two point sources at the same time and the results obtained by directly analyzing P waveform records of the main shock are introduced, some related problems are also discussed. The Wuding earthquakes of October, 1995 and the Lijiang earthquake are considered to be the manifestation of the same dynamic process at different temporal and spatial points and the occurrence order of the two earthquakes is related to the direction of dynamics transmission.
文摘In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.
基金Project(51005238)supported by the National Natural Science Foundation of China
文摘To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金Supported by the SF of Jiangsu Province Education(07KJB110115)
文摘In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.
文摘Denote by M the 'second main term' attached to the Siegel zeros of Dirichlet L-functions in odd Goldbach problem. Let N≥exp(exp(9.873)) be a real number, r=logN, the statement M≤0.032 N^2r^(-3) is proved in this paper.
基金Supported by the Natural Science Foundation of Anhui Province(1908085QA09)the Natural Science Research Project of Anhui Province(KJ2019A0591&KJ2017B015)Higher Education Department of the Ministry of Education(201802358008)。
文摘In this paper,the boundary knot method is applied to simulate inverse problems of determining physical boundary occurring in an inaccessible interior part.This is fulfilled from measurements of the partially accessible outer boundary.The truncated singular value decomposition under parameter choice of the cross validation method is employed for noisy boundary data cases.Numerical results for two benchmark problems show that the boundary knot method is simple,accurate,stable and computationally efficient for inverse problems under domains with doubly connected domains.
文摘In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.
