Algebraic models of connected homotopy 3-types such as quadratic modules, 2-crossed modules, crossed squares, and their relations are studied in various ways. In this work, we obtain another natural equivalence for quadratic modules. That is, we define functors between quadratic modules and our candidate category.

In this paper; free quadratic modules and totally free objects in the category of quadratic modules are constructed over Lie algebras. We use the free quadratic modules of Lie algebras to show that the category of quadratic module of Lie algebras is a co…bration category by means of Baues.

In this work, we construct a relationship between matched pairs and triples of groupoids. Given two 3groupoids with a common edge, we construct a triple groupoid by using the matched pairs actions.

In this study, the basic concepts are given in the first part. Then we gave the definition of separation axioms with Near Soft topology space. We have show that the axioms of being a Near Soft topology are satisfied with the Kuratowski closure operator

In this article, the exact solutions of the (1+1)-dimensional (DLW) equation, a fractional partial differential equation in conformable sense, which is a nonlinear, are given. Furthermore, with the aid of the mathematica program it is seen that the analytical solutions revealed with the auxiliary equation method satisfies the equation.