Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

Let  be a commutative ring with identity and  be an -module. In this work, we present the concept of semi--maximal sumodule as a generalization of -maximal submodule.

We present that a submodule  of an -module  is a semi--maximal (sortly --max) submodule if  is a semisimple -module (where  is a submodule of ). We  investegate some properties of these kinds of modules.

The following question was raised by L.Fuchs: "what are the subgroups of an abelian group G that can be represented as intersections of pure subgroups of G ? . Fuchs also added that “One of my main aims is to give the answers to the above question". In this paper, we shall define new subgroups which are a family of the pure subgroups. Then we shall answer problem 2 of L.Fuchs by these semi-pure subgroups which can be represented as the intersections of pure subgroups.

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

The purpose of this paper is to introduce a new type of compact spaces, namely semi-p-compact spaces which are stronger than compact spaces; we give properties and characterizations of semi-p-compact spaces.

    In this paper, some new types of regularity axioms, namely pairwise quasi-regular, pairwise semi-regular, pairwise pseudo regular and pairwise regular are defined and studied in both ech fuzzy soft bi-closure spaces (  bicsp’s) and their induced fuzzy soft bitopological spaces. We also study the relationships between them. We show that in all these types of axioms, the hereditary property is satisfied under closed fs bi-csubsp of . Furthermore, we define some normality axioms, namely pairwise semi-normal, pairwise pseudo normal, pairwise normal and pairwise completely normal in both  bicsp’s and their induced fuzzy soft bitopological spaces, as well as their basic properties and the relationships between them are studied.

Let R be a Г-ring, and σ, τ be two automorphisms of R. An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]_α = [a,b]_α^(σ,τ) holds for all a,b∈R and α∈Γ. In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-ring.

In the present work the performance of semifluidized bed adsorber was evaluated for removal of phenolic compound from wastewater using commercial activated carbon as adsorbent. P-chlorophenol (4-Chlorophenol) and o-cresol (2-methylphenol) was selected as a phenolic compound for that purpose. The phenols percent removal, in term of breakthrough curves were studied as affected by hydrodynamics limitations which include minimum and maximum semifluidization velocities and packed bed formation in the column by varying various parameters such as inlet liquid superficial velocity (from U_minsf to 8U_minsf m/s), and retaining grid (sometimes referred to as adsorbent loading) to initial static bed height ratio (from 3-4.5). In

The aim of this paper is to introduce and study the concept of SN-spaces via the notation of simply-open sets as well as to investigate their relationship to other topological spaces and give some of its properties.

The main purpose of this paper is to investigate some results. When h is  -( ,δ) – Derivation on prime Γ-near-ring G and K is a nonzero semi-group ideal of G, then G is commutative .