The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized De...The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.展开更多
The rapid pace of urbanization has led to the exacerbation of issues such as urban flooding,air pollution,and ecological degradation.In this context,the natural regulatory functions of urban open green spaces have eme...The rapid pace of urbanization has led to the exacerbation of issues such as urban flooding,air pollution,and ecological degradation.In this context,the natural regulatory functions of urban open green spaces have emerged as crucial elements in mitigating these challenges.From the perspective of nature-based solutions(NBS),Chulalongkorn Centennial Park serves as a case study for in-depth analysis.The objective is to investigate the role of urban open green spaces in environmental regulation.Furthermore,the research proposes scientific strategies for planning,design,and construction to enhance the ecological service functions and natural regulatory capacities of such spaces.展开更多
In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-det...In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.展开更多
Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon i...Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.展开更多
We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSS...We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.展开更多
By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this pape...By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.展开更多
The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota...The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.展开更多
The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We ...The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.展开更多
This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted...This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.展开更多
Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an e...Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.展开更多
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinea...Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.展开更多
Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional pa...Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.展开更多
In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot＇s theory. Based on Biot＇s theory, the governing field equations for the dynamic poroelasicity are est...In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot＇s theory. Based on Biot＇s theory, the governing field equations for the dynamic poroelasicity are established in terms of solid displacement and pore pressure. A method of potentials in cylindrical coordinate system is proposed to decouple the homogeneous Biot＇s wave equations into four scalar Helmholtz equations, and the general solutions to these scalar wave equations are obtained. After that, spectral Green＇s functions for a poroelastic full-space are found through a decomposition of solid displacement, pore pressure, and body force fields. Mirror-image technique is then applied to construct the half-space fundamental solutions.Finally, transient responses of the half-space to buried point forces are examined.展开更多
The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of...The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of wall temperature and number of RSTT on the Nusselt number were studied in detail. The distributions of velocity and temperature in the 60% sucrose solution were studied and the simulated results of CD with RSTT were compared with those of the smooth tube. The influence of Rayleigh number and RSTT on the Nusselt number was conducted experimentally. The results indicate that the Nusselt number of the 60% sucrose solution obviously increased with the number of RSTT but increased inconspicuously with 2 and more twisted tapes. The simulation shows that the distance for achieving an optimal heat transfer performance is 46 times the diameter of the tube. The mechanism of the natural convection heat transfer enhancement of the 60% sucrose solution in relationship with the CD and the RSTT was analyzed, and the change of average tangential velocity with the axial distance was presented to demonstrate that the enhancement of heat transfer was realized mainly because of the increase in tangential velocity.展开更多
The contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of a half space wit...The contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of a half space with a single coating layer under a normal concentrated force on the surface. The normal pressure distribution within the contact zone is assumed as Hertzian type. The solutions are constructed using superposition principle in the form of infinite series. Through comparing with the numerical results of FEM,it can be verified that the exact solutions have a rapid convergence rate and the stresses and displacements are mainly determined by the first term,which is corresponding to the solution of homogeneous half-space under Hertzian loading. The contact radius can be predicted applying the method.展开更多
This is the second part(also the main part) of the papers with the same title.Here we will discuss the existence and uniqueness theorem for the quasi-linear SEE(Stochastic equation of evolution).We will also discuss a...This is the second part(also the main part) of the papers with the same title.Here we will discuss the existence and uniqueness theorem for the quasi-linear SEE(Stochastic equation of evolution).We will also discuss an aproximation theorem展开更多
We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonli...We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonlinear parabolic systems with three unbounded nonlinearities, in the form { b1（x,u1）/ t-div（a（x,t,u1,Du1））＋div（Ф1（u1））＋f1（x,u1,u2）=O in Q, b2（x,u2）/ t-div（a（x,t,u2,Du2））＋div（Ф2（u2））＋f2（x,u1,u2）=O in Q in the framework of weighted Sobolev spaces, where b（x,u） is unbounded function on u, the Carath6odory function ai satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function Фi is assumed to be continuous on ]R and not belong to （Lloc1（Q））N.展开更多
In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the h...In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.展开更多
In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
基金Supported by Natural Science Foundation of Jiangsu Province(No.BK20200587)。
文摘The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.
基金Sponsored by Beijing Urban Governance Research Base of North China University of Technology(2024CSZL07)。
文摘The rapid pace of urbanization has led to the exacerbation of issues such as urban flooding,air pollution,and ecological degradation.In this context,the natural regulatory functions of urban open green spaces have emerged as crucial elements in mitigating these challenges.From the perspective of nature-based solutions(NBS),Chulalongkorn Centennial Park serves as a case study for in-depth analysis.The objective is to investigate the role of urban open green spaces in environmental regulation.Furthermore,the research proposes scientific strategies for planning,design,and construction to enhance the ecological service functions and natural regulatory capacities of such spaces.
基金National Natural Science Foundation of China,Grant/Award Number:61602157Henan scientific and technological project,Grant/Award Number:242102210020Basal Research Fund,Grant/Award Number:NSFRF240618。
文摘In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.
基金supported by National Hi-tech Research and Development Program of China (863 Program,Grant No.2009AA04Z404)
文摘Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.
文摘We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.
文摘By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.
基金Supported by the Teaching Steering Committee Research Project of Higher-Learning Institutions of Ministry of Education(JZW-16-DD-15)
文摘The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences under Grant No.KJCX2-EW-J02the Natural National Science Foundation of China under Grant Nos.11121403 and 11225526
文摘The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.
文摘This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.
文摘Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
基金Supported by youth foundation of Sichuan province (1999-09)
文摘Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.
基金Supported by National Natural Science Foundation of China under Grant Nos.11071278,111471004the Fundamental Research Funds for the Central Universities of GK201302026 and GK201102007
文摘Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
基金supported by the National Natural Science Foundation of China(11172268)
文摘In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot＇s theory. Based on Biot＇s theory, the governing field equations for the dynamic poroelasicity are established in terms of solid displacement and pore pressure. A method of potentials in cylindrical coordinate system is proposed to decouple the homogeneous Biot＇s wave equations into four scalar Helmholtz equations, and the general solutions to these scalar wave equations are obtained. After that, spectral Green＇s functions for a poroelastic full-space are found through a decomposition of solid displacement, pore pressure, and body force fields. Mirror-image technique is then applied to construct the half-space fundamental solutions.Finally, transient responses of the half-space to buried point forces are examined.
基金the Major Science and Technology Projects of Guangdong Province (No. 2011A080804012)
文摘The natural convection heat transfer of a 60% sucrose solution in a vertical converging-diverging tube(CD) with regularly-spaced twisted tapes(RSTT) has been investigated numerically and experimentally. The effects of wall temperature and number of RSTT on the Nusselt number were studied in detail. The distributions of velocity and temperature in the 60% sucrose solution were studied and the simulated results of CD with RSTT were compared with those of the smooth tube. The influence of Rayleigh number and RSTT on the Nusselt number was conducted experimentally. The results indicate that the Nusselt number of the 60% sucrose solution obviously increased with the number of RSTT but increased inconspicuously with 2 and more twisted tapes. The simulation shows that the distance for achieving an optimal heat transfer performance is 46 times the diameter of the tube. The mechanism of the natural convection heat transfer enhancement of the 60% sucrose solution in relationship with the CD and the RSTT was analyzed, and the change of average tangential velocity with the axial distance was presented to demonstrate that the enhancement of heat transfer was realized mainly because of the increase in tangential velocity.
文摘The contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of a half space with a single coating layer under a normal concentrated force on the surface. The normal pressure distribution within the contact zone is assumed as Hertzian type. The solutions are constructed using superposition principle in the form of infinite series. Through comparing with the numerical results of FEM,it can be verified that the exact solutions have a rapid convergence rate and the stresses and displacements are mainly determined by the first term,which is corresponding to the solution of homogeneous half-space under Hertzian loading. The contact radius can be predicted applying the method.
文摘This is the second part(also the main part) of the papers with the same title.Here we will discuss the existence and uniqueness theorem for the quasi-linear SEE(Stochastic equation of evolution).We will also discuss an aproximation theorem
文摘We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonlinear parabolic systems with three unbounded nonlinearities, in the form { b1（x,u1）/ t-div（a（x,t,u1,Du1））＋div（Ф1（u1））＋f1（x,u1,u2）=O in Q, b2（x,u2）/ t-div（a（x,t,u2,Du2））＋div（Ф2（u2））＋f2（x,u1,u2）=O in Q in the framework of weighted Sobolev spaces, where b（x,u） is unbounded function on u, the Carath6odory function ai satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function Фi is assumed to be continuous on ]R and not belong to （Lloc1（Q））N.
文摘In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.
基金Supported by the Foundation for Outstanding Middle-Aged and Young Scientists of Shandong Province(Grant No.BS2010SF004)the National Natural Science Foundation of China(Grant No.10971179)+2 种基金a Project of Shandong Province Higher Educational Science and Technology Program(Grant Nos.J10LA53J11LA02)the Natural Science Foundation of Liaocheng University(Grant No.X09008)
文摘In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
