Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

This research was conducted to measure the safety of heat stable enterotoxin a (STa) produced by enterotoxigenic Escherichia coli, through studying its toxic effect on mice since it showed a promising effect in reducing the proliferation of colorectal cancer cells. The cytogenetic effect was determined after giving five different doses (100, 200, 400, 800 and 1600)μg/Kg in comparison with negative (phosphate buffer saline / PBS) and positive (mitomycin C/ MMC, at doses of 2 and 5μg/Kg) controls on mouse bone marrow cells by employing the following parameters: mitotic index, chromosomal aberrations and micronucleus, also, the serum level of liver functional enzymes (GOT, GPT, ALP) was recorded. In addition, lethal dose 50 (LD 50) with cert

This study is concerned with shedding light on the grammatical method of Ibn Hisham Al-Ansari (761 AH), in his explanation of Bant Souad’s poem by the poet Kaab bin Zuhair, and I included a brief description of Ibn Hisham’s life with a number of explanations of this poem, then clarified the most important features of this method The grammar represented by his reliance on hearing and presenting it to analogy with mention of types of analogy, as well as his attribution of opinions to their owners with weighting, selection and balancing, and his attention to reasoning and a number of grammatical ailments, and his approach is also distinguished by following the method of fractal.

     Tow simple, rapid and sensitive spectrophotometric methods for the determination of mesalazine in pharmaceutical preparations have been carried out. The proposed methods depend on oxidative coupling reaction of mesalazine with m-aminophenol in the existence of N-bromosuccinamide in alkaline medium (method A) and 2,6-dihydroxybenzoic acid in the existence of sodium metaperiodate in basic medium (method B) to produce colored products , show highest absorptions at 640 (nm) and 515 (nm), alternately. Beer’s law was consistent in concentrations extent of 1.25-30 and 0.5-12.5 (µg.mL^-1) with molar absorptivity of 0.36×10⁴ and 0.77×10⁴ L.mol^-1.cm<

In this paper , the CO2 laser receiver system is designed and studied, with wavelength laser 10.6 ?m in room temperature , and to evaluate the performance and discussion it via the package of optical design (ZEMAX), from its output the Spot Diagram is measured through RMS ,and from the Ray fan plot , the aberrations is found which is the normal error for the best focus named (under corrected ) , the other output was the Geometric Encircled Energy in the spot diagram . and found that the radius of spot diagram at 80% (R80%) from the total energy ,and focal shift .The designed system have high efficiency and low cost .

Single mode-no core-single mode fiber structure with a section of tuned no-core fiber diameter to sense changes in relative humidity has been experimentally demonstrated. The sensor performance with tuned NCF diameter was investigated to maximize the evanescent fields. Different tuned diameters of of (100, 80, and 60)μm were obtained by chemical etching process based on hydrofluoric acid immersion. The highest wavelength sensitivity was obtained 184.57 pm/RH% in the RH range of 30% –100% when the no-core fiber diameter diameter was 60 μm and the sensor response was in real-time measurements

In this investigation, water-soluble N-Acetyl Cysteine Capped-Cadmium Telluride QDs (NAC/CdTe nanocrystals), utilizing N-acetyl cysteine as a stabilizer, were prepared to assess their potential in differentiating between DNA extracted from pathogenic bacteria (e.g. Escherichia coli isolated from urine specimen) and intact DNA (extracted from blood of healthy individuals) for biomedical sensing prospective. Following the optical characterization of the synthesized QDs, the XRD analysis illustrated the construction of NAC-CdTe-QDs with a grain size of 7.1 nm. The prepared NAC-CdTe-QDs exhibited higher PL emission features at of 550 nm and UV-Vis absorption peak at 300 nm. Additionally, the energy gap quantified via PL and UV–Vis were 2.2 eV