Let R be an individual left R-module of the same type as W, with W being a ring containing one. W’s submodules N and K should be referred to as N and K, respectively that K ⊆ N ⊆ W if N/K <<_J (D_j (W)+K)/K, Then K is known as the D J-coessential submodule of Nin W as K⊆_ (Rce) N. Coessential submodule is a generalization of this idea. These submodules have certain interesting qualities, such that if a certain condition is met, the homomorphic image of D J- N has a coessential submodule called D J-coessential submodule.

This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

Let M be an R-module, where R be a commutative;ring with identity. In this paper, we defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of M. Let T be a submodule of M. Let K  H  M, K  is called  ET-Coessential of H in M (K⊆_ET.ce H), if     . A submodule H is called ET- coclosed in M of H has no proper coessential submodule in M, we denote by  (K⊆_ET.cc H) , that is, K⊆_ET.ce H implies that   K = H. In our work, we introduce;some properties of ET-coessential and ET-coclosed submodules of M.

The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M  be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that  .

In this paper, we introduce weak and strong forms of ω-perfect mappings, namely the -ω-perfect, weakly -ω-perfect and strongly-ω-perfect mappings. Also, we investigate the fundamental properties of these mappings. Finally, we focused on studying the relationship between weakly -ω-perfect and strongly -ω-perfect mappings.

In this paper, we provide some types of - -spaces, namely, - ( )- (respectively, - ( )- , - ( )- and - ( )-) spaces for minimal structure spaces which are denoted by ( -spaces). Some properties and examples are given.
The relationships between a number of types of - -spaces and the other existing types of weaker and stronger forms of -spaces are investigated. Finally, new types of open (respectively, closed) functions of -spaces are introduced and some of their properties are studied.

Klebseilla pneumoniae possesses many virulence factors and survival strategies to persist and overcome host defenses; one of these strategies is biofilm formation. Therefore, the aims of this study was to determine the antibacterial and antibiofilm effect of Rosmarinus officinelis L. essential oil (EO) and its effect on the genes encoding of fimbrial adhesions. The antimicrobial activity was investigated by MIC. The ability to form biofilm as well as inhibition of initial cell attachment and biofilm formation was performed. PCR was carried out to detect fimH-1 and mrkD genes of type 1 and type 3 fimbrial adhesions at different time of incubation. The study revealed that MIC value of EO was 104 μg/ml on 24 (83%) of isolates, 93% of them

The study was conducted to evaluate the antifungal activity of the aqueous and
alcoholic extract and the essential oil of E. incrassata leaves toward some biological
characteristics of the water mold S. ferax. Chemical analysis of the plant leaves using HPLC
showed the content of several active compounds included 1,8-Cineole, Terpineal, Citronellal,
Phellendrene and Citiric acid.
Treatment of the fungus growing on solid media containing different concentrations of
the extracts showed significant gradual decrease in radial growth with the increasing
concentration, and the effect varied with the different extracts.
Treatment of the fungus grown in distilled water on sesame seeds with different
concentratio