In this article the notion of soft W-Hausdorf or soft W-?2 structure in soft topological spaces is proclaimed with respect to soft pre-open sets while using the ordinary points of Soft Topology. That’s is why it is named as soft P-W-Hausdorf or soft P-W-?2 structure. Some sub-spaces of soft P-W-?2 structure is also reflected. Product of these spaces.

In this article the concept of Soft β W-?2 structure in soft bi topological spaces is introduced in different ways. Fleix Hausdorff was a German Mathematician who is supposed to be the forefather of up-to-the-minute Topology. There are many topological structures in soft topology but Hausdorff topological structure is interesting and more practical, that is why it catches our attention to the best.

Molodtsov introduced the concept of soft set, as a mathematical tool for dealing with uncertainties. In this work, we have extended the concept of soft set in hemirings. We have studied soft hemirings and investigated some structural properties of them. Finally using these structural properties, we have characterized graph with loops.

In the present article a new type of algebraic structures named as left double displacement semigroup (LDD-semigroup). The structure is enhanced toward its left double displacement group (LDD-group) and discovered some useful results about these structures. The name of the notion is due to double displacement reactions in chemistry because they have same pattern of elements arrangement.

In this paper, we want to find the analytic solution of Benjamin-Bona-Mahony (BBM) equation by using Laplace Adomian Decomposition Method. Laplace Adomian Decomposition Method is an excellent mathematical tool for solving linear and nonlinear differential equation. This method is a combination of the famous integral transform known as Laplace transform and the Adomian Decomposition Method (ADM).

In this article, the Adomian decomposition method (ADM) is applied to find the solution of HIV infection model of latently infected CD4+T cells. This method investigates the solution of ordinary differential equation which is calculated in the form of the components of an infinite series. These components can be easily calculated. The efficiency and the reliability of proposed method is demonstrated in different time intervals by numerical example. The derived results indicate that the approximate solution by using the ADM can be obtained in a more efficient way. All computations have been carried out by computer code written in Mathematica.

Let U={U (m,n) : m,n ∈ Z₊} _n≥m≥0 be the q-periodic discrete evolution family of square size matrices of order m having complex scalars as entries generated by L(C^m-valued, q-periodic sequence of square size matrices (A_n)_n∈Z+ where q≥2 is a natural number. Where the Poincare map U(q,0) is the generator of the discrete evolution family U. The main objective of this article to decompose C^m with the help of discrete evolution family. In fact we decompose C^m in two sub spaces X₁ and X₂ such that X₁ is due to the stability of the discrete evolution family and the vectors of X₁ will called stable vectors. While X₂ is due to the un-stability of discrete evolution family, and their vectors will be called unstable vectors. More precisely we take the dichotomy of the discrete evolution family with the help of projection P on C^m and we discuss different results of the spaces X₁ and X₂ .