To the problems of the slope of the early period on log-log plot is more than 1 and the data of the middle period and late period is too discrete which makes the early period of theoretical curve can not be matched and too discrete middle and later data makes too difficult for interpreters to make acute analysis.

Then the time domain and frequency domain theoretical curves of the longitudinal vibration velocity of the pile head are calculated when there appears necking or fracture in the upper part of the pile.

The capacity of casing collapse beared on three kinds of axial symmetry load was researched by energy method and curved bar theory.

By means of energy method and curved bar theory,the anti-collapse abilities of the casing with medium and thick walls are analyzed and studied respectively under the actions of 180?symmetrically-distributed concentrated load,90?evenly-distributed concentrated load and 120?evenly-distributed concentrated load.

By analyzing the discharge formulas of the seeping of isolated well among the homogeneous isotropic aquifer when the water level at the beginning is in horizontal and fixed state and no water is supplied from up and down of the well,relevant theoretical curves(well flow-functions) have been introduced.

This paper analyses the labeling process of the automatic labeling system in principle, and designs the academic curve of the labeling cam.

The behavior of the type curves is analyzed.