In this paper we establish some conditions for an almost $\pi $-domain to be a $\pi $-domain. Next $\pi $-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for $\pi $-rings.
Rock burst is a common mine disaster often accompanied with casualties and property damage. An effective and accurate method for predicting rock burst is necessary. This paper proposed a method for predicting rock burst on the basis of energy theory. Firstly, according to the laws of energy distribution in the front of coalface, the energy judgment coefficient Q is proposed, the energy is not released to the outside when Q<0, it means that the rock burst will not occurs, the energy is released to the outside when Q>0, it means that the rock burst may occur, the greater Q value is, the more energy is released to the outside when rock burst occurs. Secondly, based on the geological structure of erosion zone, the influence of the uniaxial compressive strength and pre-peak energy with the different of the height ratio, lithology, and dip angle are analyzed, it concluded that uniaxial compressive strength and pre-peak energy at the bottom of the erosion zone slope are greater and the uniaxial compressive strength and pre-peak energy at the edge of the erosion zone slope are smaller. Finally, taking the Xiaoyun Coal Mine as the engineering background, the energy judgment coefficient Q for predicting rock burst is applied. The results of the field observation are consistent with the results of the energy judgment coefficient Q. It indicates that this method can better predict the location and intensity of rock burst and provide a novel idea for preventing the occurrence of rock burst.