In this paper we introduced many new concepts all of these concepts completely
depended on the concept of feebly open set. The main concepts which introduced in
this paper are minimal f-open and maximal f-open sets. Also new types of
topological spaces introduced which called Tf min and Tf max spaces. Besides,
we present a package of maps called: minimal f-continuous, maximal f-continuous,
f-irresolute minimal, f-irresolute maximal, minimal f-irresolute and maximal firresolute.
Additionally we investigated some fundamental properties of the concepts
which presented in this paper.

    Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.   

Studying the past for its importance and connection with the present is reflected in a relative scale in the light of data and thought of the predecessors of a great nation like the Mesopotamia, where its civilization flourished and rose since the ancient times, which inspires the present with inherited meanings that might be an entity or recognized symbols in the establishment of a vision, system or architectural building. The researcher has crystallized the description of the past to enhance the vision of the present within what is required by the interior design specialty about the historical origins of education and the design of schools in the Mesopotamia, in addition to its ethnic and environmental specificity and the moral content

      In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

In this work, we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied; j = , δ, α, pre, b, β

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

Functionalized-multi wall carbon nanotubes (F-MWCNTs) and functionalized-single wall carbon nanotubes (F-SWCNTs) were well enhanced using CoO Nanoparticles. The sensor device consisted of a film of sensitive material (F-MWCNTs/CoONPs) and (F-SWCNTs/CoO NPs) deposited by drop- casting on an n-type porous silicon substrate. The two sensors perform high sensitivity to NO₂ gas at room temperatures. The analysis indicated that the (F-MWCNTs/CoONPs) have a better performance than (F-SWCNTs/CoONPs). The F-SWCNTs/CoONPs gas sensor shows high sensitivity (19.1 %) at RT with response time 17 sec, while F-MWCNTs/CoONPs gas sensor show better sensitivity (39 %) at RT with response time 13 sec. The device shows a very reproducible sensor p

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

The objective of this investigation was to study the effects of a mixture of three arbuscular mycorrhizae (Glomus etunicatum, G. leptotichum and Rhizophagus intraradices) on the development of fusarium wilt disease in tomato plants in the presence and absence of organic matter (peatmoss). Results indicated an increase in mycorrhizal root dry weight especially in the presence of the organic matter, on the other hand this parameter was significantly decreased when Fusarium oxysporum f. sp. Lycopersiciwas added simultaneously with the mycorrhiza, Moreover, mycorrhiza and organic matter significantly reduced the damping off seedling disease, disease severity and rate of infection of tomato leaves and roots caused by the pathogenic fungus, These