Characterizing hypersurfaces of generalized rotation through its normal lines;

However, it is one of the topics worthy of study that how the results of GPS survey that is based on the normal line can be converted to be compatible with the traverse survey inside tunnels that is based on the plumb line, so as to minimize the influence of the plumb line deflection on the transverse break-through accuracy of tunnels.

Use morse theory give other proof of homatopy type of CW-complex of quaterwionic projective n-space HP~n and proof that is minimal,and give scalar characteristic of normal lines of HP~n.

Based on reflection law of the light,the normal direction angle of reflect mirror in the three-dimen-sional space was deducted under the precondition of direction angles for incident light and reflect light,and the mathematic model was built,the mathematic derivation was done.

Through author s numerous practical operations,the way in employing normal in landform rectification is advanced.

Using the normal gives the differential equations and their solutions with regard to the problems of the converse proposition on the optics properties of circular cone curves, and using the normal plane explains conditional extreme value.

When light transmits through aeolotropic crystal,as far as extraordinary light is concerned,there is a smaller included angle between the ray and the wave normal in general,which is usually called walk-off angle.

It can give the direction of the wave normal and thus is convenient to calculate the optical path in crystals.

The reflection formulas of the ordinary and extraordinary light are given for determining their reflecting orientation of the wave normal and the light ray.

The refraction foumulas of the wave normal are obtained on the basis of the boundary condition of the electromagnetic wave.

With common normal line measure and approximately calculate gear thickness of worn wheel;