We studied the estimations for coneigenvalues of a matrix,introduced the concept of basic coneigenvalues,and gave some sufficient conditions to identify a nonsingular matrix by means of the constructive geometry method that defines hyperplane in real spaces.

They are identified by means of the comparison of the fingerprints of normal alkane in them,the analyses of the relative concentration distributions of normal alkane in them,the character ratios of them,and the fuzzy cluster analysis of their fingerprint information.

By the rotational isomeric state model and method, the mean-square of gyration < S~2 > for the disubstitutedpolymer chain is introduced, the characteristic ratio of < S~2 > vs.

The finite characteristic ratio L is the ratio of a material point(internal) characteristic measurement to the material or engineering structure external measurement.

In order to compare with the old methods, so-called characteristic ratio is proposed.

In this paper,the wear fault diagnosis of engines according to the discontinuous sampling,based on the principle of machine friction and wear,the fault diagnosis method of fuzzy choiceness based on proportion characteristic is promoted.