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.

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.

Urban Balance is one of the important indicators that leads to an assessment of the urbanization process in a particular country  , province or even a city that is multi-centered. By examining  the data related to Anba  province, it was found that the value of this indicator is equal to 0.96, which is less than the absolute one, and therefore the urbanization in the province is distributed collectively  

The development of a mathematical or statistical model for estimating urban growth is a complex process due to the overlap between indicators or variables that can be adopted to calculate estimate growth rates Al-Qaim city has been considered as an example to develop a statistical method by which changes

Pseudomonas aeruginosa is an opportunistic pathogen responsible for serious infections. At least three different exopolysaccharides, alginate, polysaccharide synthesis locus (Psl), and pellicle exopolysaccharide (Pel) make up the biofilm matrix in P. aeruginosa . The effect of temperature on the biofilm formation and gene expression was examined by microtiter plate and real-time quantitative polymerase chain reaction (qRT-PCR). To be able to determine the effect of temperature on biofilm formation and gene expression of P. aeruginosa, 303 clinical and environmental samples were collected. Pseudomonas aeruginosa was isolated from 61 (20.1%) and 48 (15.8%) of the clinical and e

The present study aimed to determine the genetic divergence of seven maize genotypes (Al-Maha, Sumer, Al-Fajr, Baghdad, 5018, 4 × 1 single hybrid, and 4 × 2 single hybrid) under two varied levels of nitrogen fertilization (92 and 276 kg N ha-1). The experiment occurred in 2022 in a randomized complete block design (RCBD) with a split-plot arrangement and three replications at the College of Agricultural Engineering Sciences, University of Baghdad, Iraq. The nitrogen fertilization levels served as main plots, with the maize genotypes allocated as the subplots. The results revealed that genetic variance was higher than the environmental variance for most traits, and the coefficient of phenotypic variation was close to the genetic va

        The performance of asphalt concrete pavement has affected by many factors, the temperature is the most important environmental one which has a large effect on the structural behavior of flexible pavement materials. The main cause of premature failure of pavement is the rutting, Due to the viscoelastic nature of the asphalt cement, rutting is more pronounced in hot climate areas because the viscosity of the asphalt binder which is
inversely related to rutting is significantly reduced with the increase in temperature resulting in a more rut susceptible paving mixtures. The objective of this study is to determine the effect of temperatures variations on the permanent deformation parameters (perm

In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

Methotrexate (MTX) is one of the most effective medications to treat rheumatoid arthritis (RA).Aserum of 60 Iraqi male patients suffering from RA as (G1) was newly diagnosis and the same patient in G1 after taking MTX as G2 and 40 Iraqi male healthy control as G3. Nesfatin-1 (Nf-1) is belong to the adipokine family withpleiotropic effect. Nf-1 has been found in different tissues, including stomach, pancreas, bone cells, cartilage and heart. Retinol binding protein (RBP4) was known as transpoter of retinol from its storage sites in the liver to the extrahepatic tissues. Moreover, RBP4 acts as adipokine and contributes in the pathophsyology of prototypic inflammatory disease, rheumatoid arthritis (RA). The results showed a significant increas