The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay prop...The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.展开更多
We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environmen...We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.展开更多
This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coeffici...This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.展开更多
Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic diffe...Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.展开更多
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix ...This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.展开更多
With the security problem of image information as the background, some more properties of the period of Arnold transformation of two-dimension were studied by means of introducing a integer sequence. Some new resuits ...With the security problem of image information as the background, some more properties of the period of Arnold transformation of two-dimension were studied by means of introducing a integer sequence. Some new resuits are obtained. Two interesting conjectures on the period of Arnold transformation are given. When making digital images scrambling by Arnold transformation, it is important to know the period of the transformation for the image. As the application of the theory, a new method for computing the periods at last are proposed.展开更多
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variation...In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.展开更多
In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditio...In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.展开更多
We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP)waves in an AlN-ZnO laminated composite structure.The structure is designed under the influence of the initial stresses in which one ...We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP)waves in an AlN-ZnO laminated composite structure.The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor(PSC)half-space is in welded contact with another PSC half-space.The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation,taking the initial stresses into consideration.It is shown that the incident quasi-longitudinal wave(QP-mode)at the interface generates four types of reflected and transmitted waves,namely,QP wave,quasi-transverse(QSV)wave,electric-acoustic(EA)wave,and carrier plane(CP)wave.The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure.Reflection and transmission coefficients of waves are obtained by implementing Cramer’s rule.Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.展开更多
This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on t...This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.展开更多
For lower dimensional Fermi–Pasta–Ulam（FPU） chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of th...For lower dimensional Fermi–Pasta–Ulam（FPU） chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α（t） and β（t） with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.展开更多
In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equat...In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.展开更多
In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are anal...In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.展开更多
The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton soluti...The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.展开更多
In this paper, some properties of centrosymmetric matrices, which often appear in the construction of orthonormal wavelet basis in wavelet analysis, are investigated. As an application, an algorithm which is tightly r...In this paper, some properties of centrosymmetric matrices, which often appear in the construction of orthonormal wavelet basis in wavelet analysis, are investigated. As an application, an algorithm which is tightly related to a so-called Lawton matrix is presented. In this algorithm, about only half of memory units are required and quarter of computational cost is needed by exploiting the property of the Lawton matrix and using a compression technique, it is compared to one for the original Lawton matrix.展开更多
Modern manufacturing aims to reduce downtime and track process anomalies to make profitable business decisions.This ideology is strengthened by Industry 4.0,which aims to continuously monitor high-value manufacturing ...Modern manufacturing aims to reduce downtime and track process anomalies to make profitable business decisions.This ideology is strengthened by Industry 4.0,which aims to continuously monitor high-value manufacturing assets.This article builds upon the Industry 4.0 concept to improve the efficiency of manufacturing systems.The major contribution is a framework for continuous monitoring and feedback-based control in the friction stir welding(FSW)process.It consists of a CNC manufacturing machine,sensors,edge,cloud systems,and deep neural networks,all working cohesively in real time.The edge device,located near the FSW machine,consists of a neural network that receives sensory information and predicts weld quality in real time.It addresses time-critical manufacturing decisions.Cloud receives the sensory data if weld quality is poor,and a second neural network predicts the new set of welding parameters that are sent as feedback to the welding machine.Several experiments are conducted for training the neural networks.The framework successfully tracks process quality and improves the welding by controlling it in real time.The system enables faster monitoring and control achieved in less than 1 s.The framework is validated through several experiments.展开更多
Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter...Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.展开更多
Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto＇s definition is rigorousl...Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto＇s definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.展开更多
In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The co...In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.展开更多
基金supported by the Natural Science Research Project of Anhui Educational Committee(2023AH040155)Zhisu Liu's research was supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011679+2 种基金2024A1515012704)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUG2106211CUGST2).
文摘The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.
基金partially supported by the National Natural Science Foundation of China(NSFC,11101039,11171044,11271045)a cooperation program between NSFC and CNRS of France(11311130103)+1 种基金the Fundamental Research Funds for the Central UniversitiesHunan Provincial Natural Science Foundation of China(11JJ2001)
文摘We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.
基金supported by the National Natural Science Foundation of China(11271120,11426099)the Project of Hunan Natural Science Foundation of China(13JJ3085)
文摘This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.
基金Project(06JJ30024) supported by the Natural Science Foundation of Hunan Province, ChinaProject(2004CB619206) supported by the Major State Basic Research and Development Program of China+1 种基金Project(50321402) supported by the National Science Fund for Innovative Research Groups of ChinaProject(06B052) supported by the Scientific Research Fund of Hunan Provincial Education Department of China
文摘Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.
基金This work was supported in part by the Doctor Subject Foundation of China (No. 20050533015)the National Science Foundation of China(No. 60425310,60574014).
文摘This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.
基金Project (10471020) supported by the National Natural Science Foundation project (04JJ6028) supported by the Natural Science Foundation of Hunan Province project (03A002) supported by the Ministry of Education of Hunan Province
文摘With the security problem of image information as the background, some more properties of the period of Arnold transformation of two-dimension were studied by means of introducing a integer sequence. Some new resuits are obtained. Two interesting conjectures on the period of Arnold transformation are given. When making digital images scrambling by Arnold transformation, it is important to know the period of the transformation for the image. As the application of the theory, a new method for computing the periods at last are proposed.
基金supported financially by the National Natural Science Foundation of China(10971019)supported financially by the Scientific Research Fund of Hunan Provincial Educational Department(09C852)
文摘In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11161013,11361017,and 11301106Foundation of Guangxi Key Lab of Trusted Software and Program for Innovative Research Team of Guilin University of Electronic TechnologyProject of Outstanding Young Teachers’Training in Higher Education Institutions of Guangxi
文摘In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.
文摘We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP)waves in an AlN-ZnO laminated composite structure.The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor(PSC)half-space is in welded contact with another PSC half-space.The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation,taking the initial stresses into consideration.It is shown that the incident quasi-longitudinal wave(QP-mode)at the interface generates four types of reflected and transmitted waves,namely,QP wave,quasi-transverse(QSV)wave,electric-acoustic(EA)wave,and carrier plane(CP)wave.The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure.Reflection and transmission coefficients of waves are obtained by implementing Cramer’s rule.Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.
基金the Hunan Provincial Natural Science Foundation of China(2019JJ40079,2019JJ50160)the Scientific Research Fund of Hunan Provincial Education Department(16A071,19A179)the National Natural Science Foundation of China(11701169)。
文摘This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1130110611201288+6 种基金and 11261013)the Natural Science Foundation of Guangxi Zhuang Autonomous RegionChina(Grant No.2014GXNSFBA118017)the Innovation Project of Graduate Education of Guangxi Zhuang Autonomous RegionChina(Grant No.YCSZ2014143)the Guangxi Experiment Center of Information Science(Grant No.YB1410)
文摘For lower dimensional Fermi–Pasta–Ulam（FPU） chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α（t） and β（t） with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.
基金Supported by National Natural Science Foundation of China under Grant Nos.11361017,11161013Natural Science Foundation of Guangxi under Grant Nos.2012GXNSFAA053003,2013GXNSFAA019010Program for Innovative Research Team of Guilin University of Electronic Technology
文摘In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.
基金Project supported by the Foundation of Guangxi Key Laboratory of Trusted Software, the Guangxi Natural Science Foundation, China (Grant No. 2011GXNSFA018134)the National Natural Science Foundation of China (Grant Nos. 11161013 and 61004101)
文摘In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10961011 and 60964006
文摘The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.
基金Supported by the National Natural Science Foundation of China (No. 10271021)Supported by the Postdoctor Science Foundation of China and by Excellent Youth Foundation of Educational Committee of Hunan Province respectively.
文摘In this paper, some properties of centrosymmetric matrices, which often appear in the construction of orthonormal wavelet basis in wavelet analysis, are investigated. As an application, an algorithm which is tightly related to a so-called Lawton matrix is presented. In this algorithm, about only half of memory units are required and quarter of computational cost is needed by exploiting the property of the Lawton matrix and using a compression technique, it is compared to one for the original Lawton matrix.
文摘Modern manufacturing aims to reduce downtime and track process anomalies to make profitable business decisions.This ideology is strengthened by Industry 4.0,which aims to continuously monitor high-value manufacturing assets.This article builds upon the Industry 4.0 concept to improve the efficiency of manufacturing systems.The major contribution is a framework for continuous monitoring and feedback-based control in the friction stir welding(FSW)process.It consists of a CNC manufacturing machine,sensors,edge,cloud systems,and deep neural networks,all working cohesively in real time.The edge device,located near the FSW machine,consists of a neural network that receives sensory information and predicts weld quality in real time.It addresses time-critical manufacturing decisions.Cloud receives the sensory data if weld quality is poor,and a second neural network predicts the new set of welding parameters that are sent as feedback to the welding machine.Several experiments are conducted for training the neural networks.The framework successfully tracks process quality and improves the welding by controlling it in real time.The system enables faster monitoring and control achieved in less than 1 s.The framework is validated through several experiments.
基金Project supported by the National Natural Science Foundation of China(No.10671002)the Natural Science Foundation of Hunan Province of China(No.04JJ3072)the Science Foundation of the Education Department of Hunan Province of China(No.04C383)
文摘Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10871074 and 10572011)the Natural Science Foundation of Guangxi Province,China (Grant No 0832244)
文摘Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto＇s definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005)the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244)
文摘In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.
