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In view of uncertainty of comprehensive evaluation index of security risks investigation and govern ability of coal mine, a set pair analysis and evaluation model was established. The model determines evaluation index system from two aspects of personnel factors and govern factors, taking positive and negative, similarity and dissimilarity connection degree into account to obtain a comprehensive connection degree, so as to realize quantitative evaluation of security risks investigation and govern ability of coal mine. The result of case analysis shows that the proposed model can reasonably evaluate security risks investigation and govern ability of coal mine, and the result is in line with the actual situation.

This paper discusses some spectral properties of class operators for , , , and . It is shown that if is a class operator, then the Riesz idempotent of with respect to each nonzero isolated point spectrum is selfadjoint and . Afterwards, we prove that every class operator has SVEP and property , and Weyl's theorem holds for when .

Firstly, we will show the following extension of the results on powers of -hyponormal and -hyponormal operators: let and be positive integers, if is -hyponormal for , then: (i) in case , and hold, (ii) in case , and hold. Secondly, we will show an estimation on powers of -hyponormal operators for which implies the best possibility of our results. Lastly, we will show a parallel estimation on powers of -hyponormal operators as follows: let , then the following hold for each positive integer and : (i) there exists a log-hyponormal operator such that , (ii) there exists a -hyponormal operator such that .