The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compac...The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compact and economical. A pulse with a broadened spectrum from 670 to 900 nm is generated by utilizing two 0.18-mm-thick fused silica glass plates and is used to provide two input beams for the CFWM process.The new frequency components generated from the self-phase modulation effect in the two thin glass plates contribute to the broadening of the total spectral range of the generated multicolored sidebands.展开更多
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are es...In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.展开更多
The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly d...The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.展开更多
This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For eve...This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.展开更多
基金supported by the National Natural Science Foundation of China (NSFC) (grants 61178006, 11274327and 61221064)the Recruitment Program of Global Youth Experts
文摘The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compact and economical. A pulse with a broadened spectrum from 670 to 900 nm is generated by utilizing two 0.18-mm-thick fused silica glass plates and is used to provide two input beams for the CFWM process.The new frequency components generated from the self-phase modulation effect in the two thin glass plates contribute to the broadening of the total spectral range of the generated multicolored sidebands.
文摘In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.
基金supported in part by NSF of China,N.10771142the National Basic Research Project of China,N.2005CB321701+2 种基金Shuguang Project of Shanghai Education Commission,N.08SG45Shanghai Leading Academic Discipline Project N.S30405The Fund for E-institute of Shanghai Universities N.E03004.
文摘The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.
基金supported by Program for Innovative Research Team in UIBE(No.CXTD5-05)UIBE Networking and Collaboration Center for China's Multinational Business(No.201504YY006A)+1 种基金supported by the BCMIS,NSF China Zhongdian Project(No.11131002)NSFC(No.11371062)
文摘This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.
