After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in m...After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications.Consequently,a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed.Specifically,we firstly analyze a minimum curvature equation of coordinate transformation,which possesses the characteristics of both the global and local smoothness,achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature.Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed.Meanwhile,a data structure of grid model is constructed.Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model.Using 48 433 points of 2000 National Geodetic Control Network of China,we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000,and the external positional accuracies for both models are 0.26 m and 0.03 m respectively.展开更多
Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of ...Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.展开更多
In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids....In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.展开更多
We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen tation ｜q, μ, v〉, which is defined as the eigenvector of the operator (μQ + vP), where μ and v are two realp...We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen tation ｜q, μ, v〉, which is defined as the eigenvector of the operator (μQ + vP), where μ and v are two realparameters. We also use the U operator transformation method to deal with the same problem. We obtain the normally ordered product expressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state.展开更多
基金The National Natural Science Foundation Program(41674019)The National Plan on Key Basic Research and Development of China(2016YFB0501701).
文摘After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications.Consequently,a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed.Specifically,we firstly analyze a minimum curvature equation of coordinate transformation,which possesses the characteristics of both the global and local smoothness,achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature.Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed.Meanwhile,a data structure of grid model is constructed.Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model.Using 48 433 points of 2000 National Geodetic Control Network of China,we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000,and the external positional accuracies for both models are 0.26 m and 0.03 m respectively.
基金the scientific and applied project of the Astronomical Institute of Uzbekistan with the financial support of the Academy of Sciences of the Republic of Uzbekistan
文摘Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.
文摘In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.
文摘We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen tation ｜q, μ, v〉, which is defined as the eigenvector of the operator (μQ + vP), where μ and v are two realparameters. We also use the U operator transformation method to deal with the same problem. We obtain the normally ordered product expressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state.
