1) Based on the theoretic model of algebraical prime and simple closed properties, a new short proof for quantifier elimination of the theory of complete dense binary orders was presented.

2) The second fundamental theorem of algebraical functions is fundamental and important, but it is about constant numbers, and its applicative area has a limit.

3) On the basis of B-spline, an algebraical construction of biorthonormal wavelet was proposed.

4) Method of algebraical topology used in logic synthesis attained least covering, and in order to avoid audaciousness arising, auducious problem was discussed necessarily.

5) Thus, algebraical definitions of curved lines are theorems in the method of geometry.

6) The algebraical equations obtained from the difference equations are solved by the line relaxation iterative method.

7) The singular position of similar platform 3UPU reached by algebraical method is identical to the position of general 3UPU analysized by vector method.

8) We gave a theorem on the transcendency of the limit of a sequence of algebraical functions.