摘要：The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.

摘要：Conceptual design, data model and key techniques of "Geo-engineer 3D assistant", an underground 3D GIS oriented to geology and mine application, were discussed. In particular, the importance of high-order smoothing triangular pieces to surface's fine expression in geological modeling was emphasized. The contour mode is the most favorite mode of the three modes about surface expression: DEM, TIN and contour. Topology in underground 3D modeling with CAGD was compared. From the view of boundary and coboundary, which is soul of IS 19107 (Geographic information spatial schema), 3D underground topology was re-examined.

摘要：Although numerical simulation tools are now very powerful,the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering *** the line contact structures widely used in the engineering field,few analytical models are available for predicting the mechanical behaviour when the structures deform plastically,as the classic Hertz’s theory would be ***,the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism.A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was *** proposed model was verified through an actual line contact test and a corresponding numerical *** results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.

摘要：Nowadays, more and more digitalized spatial data are sold and transmitted on the Internet. Thus, there arises an important issue about copyright protection of the digital data. To solve this problem, this paper has designed and implemented a spatial data watermarking service (SDWS) system which can provide a secure framework for data transaction and transfer via the Internet and protect the rights of both copyright owners and consumers at the same time.