In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the o...In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform c...We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.展开更多
This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. T...Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. The sunken defects proposed in this paper is a w idth abnormity defect on the FPC trace,w hich w ould cause the latent open circuit defect and affect the electrical function of circuit. The problem of flexible deformation and w idth difference make the FPC trace detection harder. Therefore,this paper proposed a detection scheme combined w ith linear masks and circle distribution characteristic. Firstly,this scheme preprocessed the acquired FPC image,divided the trace into several sub-regions and obtained the line w idth values of each trace transverse section. Then the line w idth sequences w ere searched w ith the linear difference template of gray scale. Thus,the sunken defects alternative positions w ere located. Lastly,the circle distribution characteristic is defined to identify the real defect areas from the alternative regions acquired from the previous step. Thus,the detection of sunken defects on the FPC trace w as accomplished.The algorithm w as tested in the self-built image database,w hich show s the better detection performance than the other typical algorithms.展开更多
The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simu...The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.展开更多
In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable...In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.展开更多
The problem of penetrative convection with the cubic and fifth-order equations of state proposed by Merker, Waas and Grigull is studied. Both linear instability and nonlinear stability analyses are performed to assess...The problem of penetrative convection with the cubic and fifth-order equations of state proposed by Merker, Waas and Grigull is studied. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict destabilisation of the convection. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three-dimensional simulation. The results show that the linear threshold accurately predicts the onset of instability in the basic steady state solution.展开更多
基金supported by the National Natural Science Foundation of China (11171119 and 10871076)
文摘In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
文摘We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.
基金supported by the NNSF of China(Grant No.41405083)Hunan Provincial Natural Science Foundation of China(Grant No.2015JJ3098)
文摘This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
文摘Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. The sunken defects proposed in this paper is a w idth abnormity defect on the FPC trace,w hich w ould cause the latent open circuit defect and affect the electrical function of circuit. The problem of flexible deformation and w idth difference make the FPC trace detection harder. Therefore,this paper proposed a detection scheme combined w ith linear masks and circle distribution characteristic. Firstly,this scheme preprocessed the acquired FPC image,divided the trace into several sub-regions and obtained the line w idth values of each trace transverse section. Then the line w idth sequences w ere searched w ith the linear difference template of gray scale. Thus,the sunken defects alternative positions w ere located. Lastly,the circle distribution characteristic is defined to identify the real defect areas from the alternative regions acquired from the previous step. Thus,the detection of sunken defects on the FPC trace w as accomplished.The algorithm w as tested in the self-built image database,w hich show s the better detection performance than the other typical algorithms.
基金supported by the Iraqi ministry of higher education and scientific research
文摘The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.
文摘In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.
文摘The problem of penetrative convection with the cubic and fifth-order equations of state proposed by Merker, Waas and Grigull is studied. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict destabilisation of the convection. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three-dimensional simulation. The results show that the linear threshold accurately predicts the onset of instability in the basic steady state solution.
