mid value
2.Based on the Rolle mid-value theorem, by using determinant method, the Lagrange mid-value theorem and Cauchy mid-value theorem are obtained, and some new results are discovered.
5.The main results as following:A RIL populations derived from Jiafuzhan×MInghui86 (abbr: MJ86) was constructed, which the number of individuals is 390. Phenotyping shows that the average value of GL, GW and L/W are very close to mid-parent value, without super-parent value in the population, the average value of WE is also very close to mid-parent value but with super-parent value.
8.Results of the computation along the whole span of SRC beam showed that the values of mid-span moment, strain and deformation are maximum, while the mid-span slip value is minimum.
9.3. the low velocity layer exists in a very wide range of the mid-crust. The lowest velocity value is near 5.60 km/s;
10.The theorem on asymptotic behavior of the "mid-point" in Taylor mean value theorem involving the Lagrange remainder given by Alfonso G. Azpeitia having been generalized in this technique, the problem of asymptotic behavior of the "mid-point" in the theorem is solved to a great extent.

