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.

A class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented 2017, later in 2022, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept

      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

This study is concerned with channel banks slopes in the middle sector of Al-Massab Al-Aam channel in the middle and south of Iraq. The geotechnical properties of soil in the channel banks including physical ,engineering, chemical and mineralogical characters in over (25) station have been studied.
The grain size distribution of the bank soils of channel showed that the clay percentage is higher than those of the silt and sand percentages.
The bank soils are classified according to the USCS standards. They are composed of clay with low plasticity (CL) that represents 88% of the soil and ,clay with high plasticity (CH)represents 12% of the soil. The saturated density values ranges between 1.679 and 1.953 g/cm3 with average value of

 Rheumatoid arthritis (RA) was a chronic inflammatory autoimmune disease for long-term that primarily affects small joints and leads to chronic inflammation in synovial. The aimed of the study to identify the relationships among some serological markers (antibodies to citrullinated protein/peptide antigens (ACPAs), anti-mutated citrullinated vimentin (anti-MCV), anti-carbamylated protein (Anti-Carp), anti- heterogeneous nuclear ribonucleoproteins (anti-hnRNP) and Glucose-6-phosphate isomerase (GPI)) and early diagnosis of RA. The study involved (60) Patients of newly diagnosis with RA that divided in to two subgroups (30 RF positive and 30 RF negative) groups and 30 subjects as healthy control group. The serological data from serum

Pregnancy   is one of the cases that lead to immune compression, therefore the women are exposed to different types of infections and may sequel to miscarriage. Toxoplasma gondii and urinary tract infection (UTI) are the most prevalent infectious agents in human and  have a worldwide distribution. IFN-γ and TNF-α are pro inflammatory cytokine play important role in miscarriage. This study focuses on the determination, type of aerobic bacteria , concentration of IFN-γ and TNF-α among (75) abortive women and  their relation with miscarriages  . The results indicated that S.aures was the most prevalence bacteria isolated from  aborted women infected with UTI or  compensation with toxo