The necessary and sufficient conditions of the sub positivedefinite solution to the generalized unified algebraic Lyapunov equation based on Delta operator are given,the iterative algorithms for computing the sub positive-definite solution to the GUALE is established and we use numerical example to show the results.

It was showed that a generalized algebraic lattice is isomophic to the closed set lattice of some topological space if and only if it is additive.

This paper discussed a class of generalized Lie algebra:τ-Lie algebras, which are the generalization of the Lie algebras, the Lie superalgebras and the ε Lie algebras , and then introduced the conceptions of the enveloping algebra of a L, graded associative algebras G (which is correlative to L) and the τ-symmetric algebra S.

The definition of formal deductive system PL* corresponding to pseudo-R0algebras and some important properties of formal deductive system PL* are given.