In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

An experimental study was conducted on pressure drop of water flow through vertical cylindrical packed beds in turbulent region and the influence of the operating parameters on its behavior. The bed packing was made of spherical and non-spherical particles (spheres, Rasching rings and intalox saddle) with aspect ratio range 3.46  D/dp  8.486 obtaining bed porosities 0.396 0.84 and Reynolds number 1217  21758. The system is consisted of 5 cm inside diameter Perspex column, 50 cm long; distilled water was pumped through the bed with flow rate 875, 1000, 1125, 1250,1375 and 1500 l/h and inlet water temperature 20, 30, 40 and 50 ˚C. The packed bed system was monitored by using LabVIEW program, were the result

An essential tool for studying the web is its ability to show how energy moves through an ecosystem. Understanding and elucidating the relationship between species variety and their placement within the inclusive trophic dynamics is also beneficial. A food web ecological model with prey and two rival predators under fear and wind flow conditions is developed in this article. The boundedness and positivity of the system’s solution are established mathematically. The stability and existence constraints of the system’s equilibria are examined. The proposed system’s persistence limitations are established. Additionally, the bifurcation analysis of every potential equilibrium is examined using the Sotomayor theorem. To describe the

The acidity of spent lubricant was treated using sodium hydroxide solution. The effect of three variables on the treatment have been studied . These are mixing time rangingfrom 5-35 minutes, NaOH to lubricant weight ratio ranging from  0.25-1.25 and weight percentage  of NaOH ranging from  2-6 % .

The experimental design of Box-Wilson method is adopted to find a useful relationship between the three controllable variables and the lowering in the acidity of the spent lubricant. Then the effective variables and interactions are identified using the statistical analysis(F-test) of  three variable fractional design. The mathematical model is well represented  by a second order polynomial.

By

Background: Coronavirus pandemic (COVID-19) has enormously affected various healthcare services including the one of community pharmacy. The ramifications of these effects on Iraqi community pharmacies and the measures they have taken to tackle the spread of COVID-19  is yet to be explored. In this cross sectional survey, infection control measures by community pharmacies in Sulaimani city/Iraq has been investigated.        

Methods: Community pharmacists were randomly allocated  to participate in a cross-sectional survey via visiting their pharmacies and filling up the questionnaire form.

Results and discussion:

         In this study some generic commercial products of Atorvastatin tablets were evaluated by dissolution test in acid medium by comparing with that of parent drug Lipitor of Pfizer Company. Some of solubilizing agents were studied in formulation  of Atorvastatin tablet including;  surface active agent  and PEG 6000 .The most effective factor was the  use of PEG6000 in formulation of Atorvastatin tablet which improved the dissolution and the results of dissolution profile of formulated tablet in this work  was bioequivalent to that of Lipitor .The quantitative analysis of this work was performed by using reversed phase liquid chromatography and a proper mixture of &nbsp

The Corrosion protection effectiveness of Alimina(Al2O3,50nm)and Zinc oxide (ZnO,30nm) nanoparticales were studied on carbon steel and 316 stainless steel alloys in saline water (3.5%NaCl)at four temperatures: (20,30,40,50 OC)using three electrodes potentiostat. An average corrosion protection efficiencies of 65 %and 80% was achieved using Al2O3 NP's on carbon steel and stainless steel samples respectively, and it seems that no effect of rising temperature on the performances of the coated layers. While ZnO NP'S showed protection efficiency around 65% for the two alloys and little effected by temperature rising on the performanes of the coated layers. The morphology of the coated spesiemses was examined by Atomic force microscope.