Abstract: On the power unit vector presented by Yang Wenxiong, it for the mathematical theory of k multiplier is extended to create a new mathematical branch. The extended k multiplier is yet to concern the negative powers. Enumerating the combinatorial variaties and its functions can satisfy the various conditions, formulas, integrations, and equations etc. derived by Yang Wenxiong. The theory of k multiplier will be applied further to establish the theory of supperlight of a particle and its motion with the natural wave-particle duality etc.

Key words: power unit vector, k multiplier, hyperbolic function, hyperbolic equation