一种基于模糊正域类的模糊属性约简方法

为了实现模糊信息系统属性约简问题,探讨一种基于正域类的模糊属性约简方法。利用模糊二元相似关系建立模糊相似类的方法,进而定义决策属性关于条件属性的模糊正域类,得到正域类属性的重要度。结果表明:一方面,实现模糊信息系统属性约简;另一方面,通过取不同的相似精度,得到不同属性约简集。     

具有精确色散性的非线性波浪水平二维数学模型

建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。     

On a power series solution to the Boussinesq equation

For certain initial and boundary conditions the Boussinesq equation, a nonlinear partial differential equation describing the flow of water in unconfined aquifers, can be reduced to a boundary value problem for a nonlinear ordinary differential equation. Using Song et al.'s (2007) [7] approach, we show that for zero head initial condition and power-law flux boundary condition at the inlet boundary, the solution in the form of power series can be obtained with Barenblatt's (1990) [2] rescaling procedure applied to the power series solution obtained in Song et al. (2007) [7] for the power-law head boundary condition. Polynomial approximations can then be obtained by taking terms from the power series. Although for a small number of terms the newly obtained approximations may be worse than polynomial approximations obtained by other techniques, any desired accuracy can be achieved by taking more terms from the power series.     

Stationary phase approximation in the ambient noise method revisited

The method of extracting Green's function between stations from cross correlation has proven to be effective theoretically and experimentally.It has been widely applied to surface wave tomography of the crust and upmost mantle.However,there are still controversies about why this method works.Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space,and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green's function.His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green's function.However,his derivation ignores influence from the two stationary points at infinities,therefore it may fail when attenuation is absent.In order to obtain accurate noise-correlation function due to scatters over the whole space,we compute the total contribution with numerical integration in polar coordinates.Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function,in both amplitude and phase,when the frequency is low with reasonable quality factor Q.Our results argue that the distance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method,and only the station pairs whose distances are above several (5) wavelengths can be used.     

Point- and curve-based geometric conflation

Geometric conflation is the process undertaken to modify the coordinates of features in dataset A in order to match corresponding ones in dataset B. The overwhelming majority of the literature considers the use of points as features to define the transformation. In this article we present a procedure to consider one-dimensional curves also, which are commonly available as Global Navigation Satellite System (GNSS) tracks, routes, coastlines, and so on, in order to define the estimate of the displacements to be applied to each object in A. The procedure involves three steps, including the partial matching of corresponding curves, the computation of some analytical expression, and the addition of a correction term in order to satisfy basic cartographic rules. A numerical example is presented.     

Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions

The spectral representation method(SRM) is widely used to simulate spatially varying ground motions.This study focuses on the approximation approach to the SRM based on root decomposition,which can improve the efficiency of the simulation.The accuracy of the approximation approach may be affected by three factors: matrix for decomposition,distribution of frequency interpolation nodes and elements for interpolation.The influence of these factors on the accuracy of this approach is examined and the following conclusions are drawn.The SRM based on the root decomposition of the lagged coherency matrix exhibits greater accuracy than the SRM based on the root decomposition of the cross spectral matrix.The equal energy distribution of frequency interpolation nodes proposed in this study is more effective than the counter pith with an equal spacing.Elements for interpolation do not have much of an effect on the accuracy,so interpolation of the elements of the decomposed matrix is recommended because it is less complicated from a computational efficiency perspective.     

TTI介质qP波逆时偏移中伪横波噪声压制方法

在对地下复杂构造介质,特别是盐丘侧翼及岩下区域进行成像时,相对于传统的各向同性逆时偏移和VTI逆时偏移,具有倾斜对称轴的TTI逆时偏移成像效果最优.不仅反射同相轴更加的连续,而且能量得到了更好的聚焦.传统的各向异性介质全弹性波RTM的计算量大且计算效率低.由于目前仍以纵波勘探为主,因此TTI逆时偏移qP波波动方程的选取显得尤为重要.为了提高计算效率,采用将沿着对称轴方向的横波速度设为零的方法,简化得到qP波波动方程.然而,这样会引入一种严重影响成像效果的低速度、低振幅的qSV波人为干扰.本文建立了qP波方程的完全匹配层控制方程,而后借助于辅助波场采用一种高效的压制伪横波噪声传播的方法,通过模型测试验证了该方法的有效性.     

On the impossibility of mean-field dynamos with some spherical symmetry of the motions

Abstract

A spherical mean-field dynamo model is considered in which both the mean motion and the mean electro-motive force due to fluctuating motions show some spherical symmetry. It is shown that under some reasonable assumptions the magnetic field is bound to decay to zero.     

A review of: “Problems of Solar and Stellar Oscillations. Iau Colloquium No. 66. Edited by D. O. Gough. D. Reidel Publishing Company, 493 pp. Df1195.00/U.S. $84.50 (ISBN 90-277-1554-8). 1983.”

Abstract

The model equations describing two-dimensional thermohaline convection of a Boussinesq fluid in a rotating horizontal layer are known to support multiple instabilities, depending on the values of certain control parameters (Arneodo et al., 1985). Most of these multiple instabilities have already been studied for double or triple diffusive convection, where behaviours ranging from simple steady to irregular motions have been found. Here we consider the one remaining bifurcation mentioned by Arneodo et al. (1985): the interaction between a steady and an oscillatory convection roll when the linear spectrum for a single wavenumber comprises one zero and one pair of purely imaginary eigenvalues. The method of centre manifolds and normal forms is used to derive evolution equations for the amplitudes of the convection rolls close to bifurcation and the behaviours associated with the equations is discussed.