Narrow Results

The main purpose of this paper is to study Jacobi–Jordan-admissible algebras and some particular classes like pre-Jacobi–Jordan algebras. First, we provide characterizations of Jacobi–Jordan algebras by means of oxidation process. Then, we discuss Jacobi–Jordan-admissible algebras for which we obtain a surprising characterization as 3-power anti-associative algebras. Moreover, we introduce a concept of $\lambda$-anti-associative algebra, generalizing anti-associative algebras and prove that they are equivalent to Jacobi–Jordan-admissible algebras. Furthermore, we study the structure of pre-Jordan–Jacobi algebras which form a particular class of Jacobi–Jordan-admissible algebras. Moreover, an inductive description by a process of oxidation is provided for an interesting particular class of pre-Jacobi–Jordan algebras, called strong pre-Jacobi–Jordan algebras.

Nitride doped titanium oxide (TiO_xN_y) is a photocatalytic material which acts under visible light, while conventional titanium oxide acts only in ultra violet light. In this study, we tried to make nitride doped titanium film by oxidizing of TiN film. The TiN films were deposited on the quartz substrate by DC magnetron sputtering. The film structure was analyzed by X-ray diffraction. The photocatalytic decomposing rate was measured using methylene blue solution under black light and fluorescent lamp. As a result, post annealing process after oxidizing process is unsuitable to realize a high photocatalytic activity for oxidized TiN. On the other hand, the samples oxidized in nitrogen rich atmosphere showed the obvious photocatalytic activity under visible light irradiation. This reason is that the oxidation of the film surface is controlled and nitrogen atom left in film surface by nitrogen gas supplying. In conclusion, oxidizing of TiN film in nitrogen rich atmosphere is suitable to realize a high photocatalytic activity.