Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating sp...Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating splitting shear-wave phases and its reliability byusing of the assumption that variance of noise and useful signal data obey normaldistribution.To check the validity of new method,the identification results and errorestimation corresponding to 95% confidence level by analyzing simulation signals have beengiven.展开更多
In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with ...In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with their Euler-Maclaurin asymptotic expansions of the errors. The presented method is suit for solving multidimensional and singular integrals by comparing with Gauss quadrature rule. The error asymptotic expansions show that the convergence order of the initial quadrature rules is , where . The order of accuracy can reach to by using extrapolation and splitting extrapolation, where h0 is the maximum mesh width. Some numerical examples are constructed to show the efficiency of the method.展开更多
Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with ...Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.展开更多
The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solut...The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.展开更多
The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In conside...The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.展开更多
基金This project was sponsored by the National Science Foundation of China (49734150) and the Join Earthquake Science Foundation of China Seismological Burear(198061).
文摘Based on the propagation characteristics of shear wave in the anisotropic layers,thecorrelation among several splitting shear-wave identification methods hasbeen studied.Thispaper puts forward the method estimating splitting shear-wave phases and its reliability byusing of the assumption that variance of noise and useful signal data obey normaldistribution.To check the validity of new method,the identification results and errorestimation corresponding to 95% confidence level by analyzing simulation signals have beengiven.
文摘In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with their Euler-Maclaurin asymptotic expansions of the errors. The presented method is suit for solving multidimensional and singular integrals by comparing with Gauss quadrature rule. The error asymptotic expansions show that the convergence order of the initial quadrature rules is , where . The order of accuracy can reach to by using extrapolation and splitting extrapolation, where h0 is the maximum mesh width. Some numerical examples are constructed to show the efficiency of the method.
基金Hundred Talent Program of Chinese Academy of Sciences under Grant No. 0300YQ000101. Partly supported by the National Natural Sci
文摘Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.
基金the National Sciences Foundation of China and the Doctorial Program of Higher Edua-tion
文摘The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.
基金supported by the Natural Science Foundation of China (51175423)
文摘The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.
