This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t...This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.展开更多
Reading is the main way of acquiring information and an important method of learning foreign language. But in the reading process, because of the affective and cognitive differences and the lack of knowledge about rea...Reading is the main way of acquiring information and an important method of learning foreign language. But in the reading process, because of the affective and cognitive differences and the lack of knowledge about reading patterns and methods, undergraduates＇ reading efficiency and speed are greatly influenced. This article analyzes the mode and strategies which can be adopted in English reading.展开更多
An effective statistical downscaling scheme was developed on the basis of singular value decomposition to predict boreal winter(December-January-February)precipitation over China.The variable geopotential height at 50...An effective statistical downscaling scheme was developed on the basis of singular value decomposition to predict boreal winter(December-January-February)precipitation over China.The variable geopotential height at 500 hPa(GH5)over East Asia,which was obtained from National Centers for Environmental Prediction’s Coupled Forecast System(NCEP CFS),was used as one predictor for the scheme.The preceding sea ice concentration(SIC)signal obtained from observed data over high latitudes of the Northern Hemisphere was chosen as an additional predictor.This downscaling scheme showed significantly improvement in predictability over the original CFS general circulation model(GCM)output in cross validation.The multi-year average spatial anomaly correlation coefficient increased from–0.03 to 0.31,and the downscaling temporal root-mean-square-error(RMSE)decreased significantly over that of the original CFS GCM for most China stations.Furthermore,large precipitation anomaly centers were reproduced with greater accuracy in the downscaling scheme than those in the original CFS GCM,and the anomaly correlation coefficient between the observation and downscaling results reached～0.6 in the winter of 2008.展开更多
In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. U...In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution.展开更多
Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom ...Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.展开更多
In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a dou...In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.展开更多
It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to fur...It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.展开更多
In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz esti...In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.展开更多
We investigate theoretically the intervalley plasmon excitations(IPEs) in graphene monolayer within the random-phase approximation. We derive an analytical expression of the real part of the dielectric function. We fi...We investigate theoretically the intervalley plasmon excitations(IPEs) in graphene monolayer within the random-phase approximation. We derive an analytical expression of the real part of the dielectric function. We find a lowenergy plasmon mode with a linear anisotropic dispersion which depends on the Fermi energy and the dielectric constant of substrate. The IPEs show strongly anisotropic behavior, which becomes significant around the zigzag crystallographic direction. More interestingly, the group velocity of IPE varies from negative to positive, and vanishes at special energy.展开更多
文摘This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
文摘Reading is the main way of acquiring information and an important method of learning foreign language. But in the reading process, because of the affective and cognitive differences and the lack of knowledge about reading patterns and methods, undergraduates＇ reading efficiency and speed are greatly influenced. This article analyzes the mode and strategies which can be adopted in English reading.
基金supported by the China Meteorological Special Project(GYHY201206016)the National Basic Research Program of China(2010CB950304)the Innovation Key Program of the Chinese Academy of Sciences(KZCX2-YW-QN202)
文摘An effective statistical downscaling scheme was developed on the basis of singular value decomposition to predict boreal winter(December-January-February)precipitation over China.The variable geopotential height at 500 hPa(GH5)over East Asia,which was obtained from National Centers for Environmental Prediction’s Coupled Forecast System(NCEP CFS),was used as one predictor for the scheme.The preceding sea ice concentration(SIC)signal obtained from observed data over high latitudes of the Northern Hemisphere was chosen as an additional predictor.This downscaling scheme showed significantly improvement in predictability over the original CFS general circulation model(GCM)output in cross validation.The multi-year average spatial anomaly correlation coefficient increased from–0.03 to 0.31,and the downscaling temporal root-mean-square-error(RMSE)decreased significantly over that of the original CFS GCM for most China stations.Furthermore,large precipitation anomaly centers were reproduced with greater accuracy in the downscaling scheme than those in the original CFS GCM,and the anomaly correlation coefficient between the observation and downscaling results reached～0.6 in the winter of 2008.
文摘In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution.
文摘Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system.
基金Supported by the National Science Council of the Republic of China under Grant No.NSC101-2115-M-126-002the National Natural Science Foundation of China under Grant No.11371241Project of "The First-class Discipline of Universities in Shanghai"
文摘In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.
基金supported in part by the National Science Foundation of China under Grant No. 10771116the Doctoral Program of the Ministry of Education under Grant No. 20060003003
文摘It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.
基金the Graduate Student Innovation Fund of Fudan University.
文摘In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.
基金Supported by the National Basic Research Program of China(973 Program)under Grant No.2013CB934001the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-2013ZX-28
文摘We investigate theoretically the intervalley plasmon excitations(IPEs) in graphene monolayer within the random-phase approximation. We derive an analytical expression of the real part of the dielectric function. We find a lowenergy plasmon mode with a linear anisotropic dispersion which depends on the Fermi energy and the dielectric constant of substrate. The IPEs show strongly anisotropic behavior, which becomes significant around the zigzag crystallographic direction. More interestingly, the group velocity of IPE varies from negative to positive, and vanishes at special energy.
