The method of killing tumor cells by focused bi-frequency ultrasound activated hematoporphyrin derivatives is presented and evaluated in this paper.

UDC 512.5 Let ℛ be a unital * -ring with the unit I . Assume that ℛ contains a symmetric idempotent P which satisfies A ℛ P = 0 implies A = 0 and A ℛ ( I - P ) = 0 implies A = 0 . In this paper, it is proved that if ϕ : ℛ → ℛ is a nonlinear skew commuting map, then there exists an element Z ∈ 𝒵 S ( ℛ ) such that ϕ ( X ) = Z X for all X ∈ ℛ , where 𝒵 S ( ℛ ) is the symmetric center of ℛ .As an application, the form of nonlinear skew commuting maps on factors is obtained.