Because of the non-completion of the concepts of regularity in some textbooks on mathematical analySis and differentical geometry,this paper investigate the geometrical characteristics and decisive methods of all types of non -regular points on curves according to the concepts of regular curves.

The paper shows, that the condition "X is a homeomorphism" of the definition of a regular surfaces can be substituted with the condition "X is One-to-one".

The design of curvature correction temperature compensation bandgap reference circuit use the first order temperature compensation bandgap reference voltage as a curvature voltage, and get a better circuit though designing a circuit can produce a I2PTAT current than usually use PTAP voltage as a curvature voltage, which is fabricated with 0.

In this paper, a double equation model incorporating the method of curvature correction is developed to closure the Reynolds stress and the SIMPLEC scheme is used to discrete turbulent governing equation.

Both standard k-ε model and its curvature correction version have been used in calculations.

The existence of collapsed metrics on S7 with positive curvature is proved.

By the definitions of the conjugate point and the focal point in a geodesic,the paper proves that for any geodesic γ:［0,+∞)→M,in a complete Gauss surface M with positive curvature,there exists t＞0 such that γ(t) is a focal point of γ(0).