In this paper. it is discussed that the absohue stability for zero solution of thediscrete type Lurie control systmin which the nonlinear function f(σ) satisfying conditions as followsIt gives the necessary and suffi...In this paper. it is discussed that the absohue stability for zero solution of thediscrete type Lurie control systmin which the nonlinear function f(σ) satisfying conditions as followsIt gives the necessary and sufficent conditions for the absolute stability forystem (I) under conditions (2).We also obtain the sufficient criteria for absolutesiability of the simplified system of (I) under conditions (3) .展开更多
In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control systemin which the nonlinear function f(σ)satisfying conditions followsIt gives the necessary and sufficient condi...In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control systemin which the nonlinear function f(σ)satisfying conditions followsIt gives the necessary and sufficient conditions for the absolute stability for system (1) under conditions (2).We also obtain the sufficient for absolute stability of the simplified system of (1) under conditions (3) .展开更多
By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ...By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.展开更多
In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well...In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.展开更多
The aim of the present investigation was to research the distribution characteristics of copper in water and sediment of the Liao River, China. The concentrations of copper in water and sediment showed significant dif...The aim of the present investigation was to research the distribution characteristics of copper in water and sediment of the Liao River, China. The concentrations of copper in water and sediment showed significant difference at different sampling stations. The distribution characteristics of copper in water and sediment were obtained by using discrete and continuous numerical characteristics. The results indicated that the average concentrations of copper in water and sediment decreased slightly after its accumulation. While the deviations of the concentrations of copper in water and sediment from the expectation increased significantly after its accumulation. The skewness distributions of the concentrations of copper in water and sediment did not change much before and after its accumulation. The kurtosis distributions of the concentrations of copper in water and sediment decreased significantly after its accumulation. Therefore, the precise distribution characteristics of copper in water and sediment were obtained through the combination of the discrete and continuous numerical characteristics. .展开更多
We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.A...We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched.展开更多
In this paper, we use Hermite weighted essentially non-oscillatory （HWENO） schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reco...In this paper, we use Hermite weighted essentially non-oscillatory （HWENO） schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes （HWENO-RK） of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.展开更多
In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computa...In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computational requirements are greatly reduced without assuming more regularities on the solution u.展开更多
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is li...This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.展开更多
文摘In this paper. it is discussed that the absohue stability for zero solution of thediscrete type Lurie control systmin which the nonlinear function f(σ) satisfying conditions as followsIt gives the necessary and sufficent conditions for the absolute stability forystem (I) under conditions (2).We also obtain the sufficient criteria for absolutesiability of the simplified system of (I) under conditions (3) .
文摘In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control systemin which the nonlinear function f(σ)satisfying conditions followsIt gives the necessary and sufficient conditions for the absolute stability for system (1) under conditions (2).We also obtain the sufficient for absolute stability of the simplified system of (1) under conditions (3) .
基金Supported by National Natural Science Foundation of China(Grant No.12071491)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.
基金a HKU Seed grant the Research Grants Council of the Hong Kong SAR(HKU7016/07P)
文摘In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.
文摘The aim of the present investigation was to research the distribution characteristics of copper in water and sediment of the Liao River, China. The concentrations of copper in water and sediment showed significant difference at different sampling stations. The distribution characteristics of copper in water and sediment were obtained by using discrete and continuous numerical characteristics. The results indicated that the average concentrations of copper in water and sediment decreased slightly after its accumulation. While the deviations of the concentrations of copper in water and sediment from the expectation increased significantly after its accumulation. The skewness distributions of the concentrations of copper in water and sediment did not change much before and after its accumulation. The kurtosis distributions of the concentrations of copper in water and sediment decreased significantly after its accumulation. Therefore, the precise distribution characteristics of copper in water and sediment were obtained through the combination of the discrete and continuous numerical characteristics. .
文摘We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched.
基金Research partially supported by NNSFC grant 10371118,SRF for ROCS,SEM and Nanjing University Talent Development Foundation.
文摘In this paper, we use Hermite weighted essentially non-oscillatory （HWENO） schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes （HWENO-RK） of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.
文摘In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computational requirements are greatly reduced without assuming more regularities on the solution u.
基金This work is supported by NSFC(Grant Nos.11771035,11771162,11571128,61473126,91430216,91530204,11372354 and U1530401),a grant from the RGC of HK 11300517,China(Project No.CityU 11302915),China Postdoctoral Science Foundation under grant No.2016M602273,a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province,and the USA National Science Foundation grant DMS-1315259the USA Air Force Office of Scientific Research grant FA9550-15-1-0001.Jiwei Zhang also thanks the hospitality of Hong Kong City University during the period of his visiting.
文摘This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.
