The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop...The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.展开更多
The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit,...The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.展开更多
The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the a...The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the above problem are given.展开更多
According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution i...According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.展开更多
基金supported by the National Science and Technology Major Projects(No.2011ZX05020-008)Well Logging Advanced Technique and Application Basis Research Project of Petrochina Company(No.2011A-3901)
文摘The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10774120 and 10975114the Natural Science Foundation of Gansu Province under Grant No.1010RJZA012Natural Science Foundation of Northwest Normal University under Grant No.NWNU-KJCXGC-03-48
文摘The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.
文摘The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the above problem are given.
基金supported by the National Natural Science Foundation of China(Grant Nos.11272346)the National Basic Research Program of China("973"Project)(Grant No.2013CB733100)
文摘According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.