ASSESSMENT OF THE EFFECTIVE RANK OF A (CO)VARIANCE MATRIX: A NON-PARAMETRIC GOODNESS-OF-FIT TEST

Each eigenvector of the dispersion matrix[X]~T[X]was shown to be a partial predictor of the originaldata matrix [X],the sum of the predictions from the individual principal components being equal to theexpectance of [X].By comparing the distributions of the members of two neighbouring predictedmatrices,[X]_(1...i)and [X](1...i+1)(i.e.the sums of the first i and i+1 individual predictions respectively),it was shown that they should be indistinguishable provided that i is equal to or greater than the effectiverank of [X],and significantly different otherwise.This was confirmed by analysing the visible absorptionspectra of methyl orange and methyl red solutions as well as the Raman spectra of Na_2SO_4 and MgSO_4solutions.On the grounds of these findings,a non-parametric goodness-of-fit test for assessing theeffective rank of[X]was proposed which proved to be comparatively conservative and more robust thanmost currently used tests.     

Self-Affine Fractals and the Fractal Dimension of Fractured Rock Profiles

The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same res     

新疆齐求Ⅰ金矿床毒砂及其在金的成矿过程中的作用

所研究的毒砂形成两个成矿阶段。成矿前阶段的毒砂具有颗粒粒大、裂隙发育和明显的成分环带等特征。成矿前的裂隙为金的迁移和沉淀提供了良好的空间。成矿期阶段的毒砂颗粒细小,无成分环带。根据形态、分布规律和成分特点,成矿期毒砂可划分为两个世代:早期的,自形程度高,无明显成分异常;晚期的,他形晶,含砷低。毒砂的特性反映了金的成矿作用的演变过程。     

平顶山矿区煤矸石特征及综合利用途径

在查明平顶山矿区煤矸石占地面积、矸石积存量及年排矸量的基础上，作者系统地采集了全矿区井上和井下煤矸石样品，进行了化学分析、工业分析、光谱分析、Ｘ射线衍射、岩矿鉴定和扫描电镜测定。查明了本矿区煤矸石的成分、矿物及微量元素特征。并指出了各类矸石可资进行综合利用的途径。