In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of...In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.展开更多
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd ...Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.展开更多
A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the densit...A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.展开更多
The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended e...The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy＇s principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.展开更多
The nonlocal symmetry for the potential Kadomtsev-Petviashvili(pKP)equation is derived by the truncated Painleve analysis.The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary depen...The nonlocal symmetry for the potential Kadomtsev-Petviashvili(pKP)equation is derived by the truncated Painleve analysis.The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable.Thanks to localization process,the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems.The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations.Based on the consistent tanh expansion method,a nonauto-B(a|¨)cklund transformation(BT)theorem of the pKP equation is constructed.We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem.Some special interaction solutions are investigated both in analytical and graphical ways.展开更多
基金Project(17D02)supported by the Open Fund of State Laboratory of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan University,ChinaProject supported by the State Key Laboratory of Satellite Navigation System and Equipment Technology,China
文摘In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.
基金The project supported by the National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province of China under Grant No. Y504111, and the Science Research Foundation of Huzhou University
文摘Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.
基金Projects(11372055,11302033)supported by the National Natural Science Foundation of ChinaProject supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology,ChinaProject(2012KFJJ02)supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle,Education Department of Hunan Province,China
文摘A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002
文摘The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy＇s principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305106,11275129 and 11405110the Natural Science Foundation of Zhejiang Province of China under Grant No.LQ13A050001
文摘The nonlocal symmetry for the potential Kadomtsev-Petviashvili(pKP)equation is derived by the truncated Painleve analysis.The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable.Thanks to localization process,the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems.The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations.Based on the consistent tanh expansion method,a nonauto-B(a|¨)cklund transformation(BT)theorem of the pKP equation is constructed.We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem.Some special interaction solutions are investigated both in analytical and graphical ways.
