Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

    The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then Ais called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

      The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

The structure of this paper includes an introduction to the definition of the nano topological space, which was defined by M. L. Thivagar, who defined the lower approximation of G and the upper approximation of G, as well as defined the boundary region of G and some other important definitions that were mentioned in this paper with giving some theories on this subject. Some examples of defining nano perfect mappings are presented along with some basic theories. Also, some basic definitions were presented that form the focus of this paper, including the definition of nano  pseudometrizable space, the definition of nano compactly generated space, and the definition of completely nano para-compact. In this paper, we presented images of nan

Sixteen species of Armored Scale insects were recorded from Baghdad city during 2001-2005. Three of these are reported here for the first time Abgrallaspis cyanophylli (Signoret, 1869), Aonidiella citrina (Craw,1870) and Chrysomphalus aonidium (Linnaeus,1758). The other thirteen species were recorded earlier Aonidiella aurantii (Maskell), Aonidiella orientalis (Newstead), Chrysomphalus dictyospermi (Morgan), Diaspidiotus ostreaeformis (Curtis), Diaspidiotu perniciosus (Comctock), Hemiberlesia lataniae (Signoret), Lepidosaphes beckii (Newman), Lepidosaphes conchiformis (Gmelin), Lepidosaphes ulmi (Linnaeus), Mercetaspis halli

The study aims to investigate the antimicrobial activity of propolis obtained from different regions of Iraq compared with that of propolis obtained from Iran. Samples were investigated for their antimicrobial activity against Staphylococcus aureus, Pseudomonas aeruginosa, Eschericha coli, Klebsiella pneumoniae, Bacillus cereus , Staphylococcus epidermidis and Candida albicans using standard antimicrobial assays. Marked variations in the antimicrobial activity of the different propolis samples were observed, the method of extraction selected gives the highest antimicrobial activity and the best alcohol concentration using in the extraction of propolis , then the crude extract of propolis showed synergistic effect with some antibiotics in

To explore the durability of some local species of wood to fungal deterioration among the
storage period, this research has conducted on three species Eufcalyptus cammaldulensis,
Juglans regia, presence of some genus of fungi; Aspergillus, Penicillium,Botryoderma,
Chaetomium, Phoma, Cladosporium and Pacilomyces in different intensities.
The two fungi Aspergillus and Penicillium appeared more dominants than others, therefore
they were chosen for the pathogenicity test. The results showed that the two species of fungi
preferred Juglans wood firstly were the size of infection was more than 10 times of any of the
other two woods. Eucalyptus showed similar response to that of Morus, but with Aspergillus
it was few bett

      This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.

In this work , we study different chaotic properties of the product space on a one-step shift of a finite type, as well as other spaces. We prove that the product  is Lyapunove  â€“unstable if and only if at least one  or  is Lyapunove  â€“unstable. Also, we show that and locally everywhere onto (l.e.o)  if and only if is locally everywhere onto (l.e.o) .