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 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

In this paper we define and study new concepts of functions on fibrewise  topological spaces  over  B namely,  fibrewise  weakly  (resp., closure, strongly) continuoac; funttions which are analogous of weakly

(resp., closure,   strongly)   continuous  functions   and  the  main  result is   : Let  <p       : XY  be a fibrewise  closure  (resp.,  weakly,  closure, strongly,  strongly) continuous function,  where  Y  is fibrewise topological  space  over  B and  X  is  a  fibrewise set  which  has  the

in

This study included the effect of chronic exposure of different concentrations of sodium chloride on the freshwater Crustacean Daphinea pulex from the order of Cladocera. The concentrations used for the chronic exposure were( 0.1‰, 0.5‰, 1‰, 1.5‰, 2‰ )to investigate the effect on the some reproductive parameter which included mean number of eggs and juveniles produced per female and per clutch,and mean number of clutch per female which decline from (6.0) clutch/female in the control treatment to (3.0) clutch/female in (2‰) concentrations, as well as to investigate the number of females produce the clutches and we found only one female produced six cluthes in the( 2‰) concentration of sodium chlor

It included the introduction to the research and its importance, as the knee joint is one of the important joints in the human body that are susceptible to injury, and among these injuries is the roughness of the knee that occurs as a result of weakness and imbalance in the work of the quadriceps muscle, so its treatment is through rehabilitation exercises to treat weakness and gain flexibility and strength.Hence the importance of the research by developing rehabilitation exercises with different resistances in the water medium and restoring flexibility and muscular strength for patients with knee roughness for ages from 30-40 years, and the experimental method was used to solve the research problem, and the research sample included (6) of

The present study was conducted to determine the effect of different concentrations of putrescine and spermidine at all stages of regeneration (callogenesis, somatic embryos multiplication, germination and rooting)) of date palm cultivar Barhee. Shoot tips were eradicated from 2-3 years old offshoots, surface sterilized and inoculated onto Murashiege and Skoog, 1962 (MS) medium supplemented with 20 mg/L 2,4-D and 3 mg/L N6-2-isopentyl adenine (2ip). Primary callus was obtained after 24 weeks on the nutrient medium. Calli were then transferred onto fresh MS medium containing 0.0, 50, 100 or 150 mg/L of putrescine or spermidine individually. Results were recorded after 12 weeks. A significant increase in embryonic callus fresh weights reached

The Isolated Combustion and Diluted Expansion (ICADE) internal combustion engine cycle combines the advantages of constant volume combustion of the Otto cycle with the high compression ratio of the Diesel cycle.   This work studies the effect of isolated air mass (charge stratification) on the efficiency of the cycle; the analysis shows that the decrease of isolated air mass will increase the efficiency of the cycle and the large dilution air mass will quench all NO_x forming reactions and reduce unburned hydrocarbons. Furthermore, the effect of Fuel / Air ratio on the efficiency shows that the increase of Fuel / Air ratio will increase efficiency of the cycle.

Background: Dental erosion is a common oral condition which results due to consumption of high caloric and low pH acidic food such as carbonated drinks and fruit juices. It is expected that these food types can cause irreversible damage to dental hard tissues and early deterioration of the dental restorations. So, this study aimed to evaluate and compare the erosive potential effects of orange fruit juice and Miranda orange drink on the microhardness of an orthodontic composite material. Materials and methods: Thirty discs with a thickness of 2 mm and a diameter of 10 mm were prepared from orthodontic bonding composite. The prepared discs were equally divided into three groups (n=10). Microhardness analysis was carried out both prior to

Background: Disinfection and shaping of the canal with a combination of chem¬ical agents and endodontic instruments play an important role in the success of endodontic therapy. Eliminating the microorganisms within the pulp space is a critical and important objective in treating a tooth with apical periodontitis. This study was conducted to evaluate the antibacterial properties of herbal alternatives (Green tea and siwak extracts) as possible irrigants during endodontic treatment compared with the conventional irrigation solutions. Materials and methods: Salvadora Persica (siwak) and Green Tea solutions were prepared.An agar diffusion test was performed on Mueller-Hinton agar using the well diffusion method. The tested solutions (5.25% N