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Due to the existence of abandoned roadways in the thick coal seam, the ground pressure would increase greatly due to the roof advanced breaking when the working face passed through the affected area of abandoned roadways. In order to solve this problem, a solution for roof presplit in the abandoned roadway was proposed. Based on the mining and geological conditions of Huasheng Hufeng coal mine, the roof vertical stress and vertical displacement with different roof presplit distance were analyzed by using FLAC3D numerical software. The research results indicated that the roof vertical stress and vertical displacement could be reduced effectively by roof presplit. When the roof presplit distance was 15 m, the maximum vertical stress and the maximum vertical displacement were both minimum. The maximum vertical stress was reduced by 14.55% and the maximum vertical displacement was reduced by 37.51% after roof presplit. The reasonable roof presplit distance of the working face was determined to be about 15 m by combining theoretical and numerical analysis. The engineering application results indicated that the maximum working resistance of the hydraulic support was reduced by 35.86% after roof presplit, and the engineering effect was good. The research results can provide technical guidance and theoretical support for the same type mines.

This paper develops a theoretical model for the optimal design of airfare as options under capacity constraint to study the price dispersion in U.S airline industry. Monopoly seller uses a menu of refund contracts to sequentially screen heterogeneous travelers who purchase the tickets before travel uncertainty is fully resolved. Airline finds it optimal to sell fully refundable fares to high-value customer when capacity is limited and to sell partially refundable fare when seats are abundant. The change of capacity accounts for the distinct jumps of non-refundable fare and the variation of refundable fare over booking periods. The model predicts that the price dispersion might fluctuate and then diminish as the number of available seat shrinks. An original data, which contains both high-frequent price and seat availability information for differentiated fares, provides strong empirical evidence that the price gap experiences step-wise drops before diminishing as departure date nears.