Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.

In this study, measuring effectiveness Alauriz in some seeds powder and found that the seeds of-sophistication sex had the highest effective enzymatic reach 353 units / gProtein and Alkabbatah study enzyme extract under different storage conditions and Altaj showed that the enzyme loses Thbatih and whether Mrkbhetwan adding Alklasrin concentration of 10% for the systematic solution

In the present work theoretical relations are derived for the efficiency evaluation for the generation of the third and the fourth harmonics u$ing crystal cascading configuration. These relations can be applied to a wide class of nonlinear optical materials. Calculations are made for beta barium borate (BBO) crystal with ruby laser /.=694.3 nm . The case study involves producing the third harmonics at X. =231.4 nm of the fundamental beam. The formula of efficiency involves many parameters, which can be changed to enhance the efficiency. The results showed that the behavior of the efficiency is not linear with the crystal length. It is found that the efficiency increases when the input power increases. 'I'he walk-off length is calculated for

Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used

The species Spongilla lacustris was identified for the first time in Iraq, it was found during winter 1998 in an irrigation canal within the campus of the University of Baghdad (Jadiriah), water is drawn from Tigris river. The specimens were found in water samples of sizes ranging between 5-50 cm with yellowish color . It was found in two habitats , one as attached on submerged aquatic plant Ceratophyllum sp., and the other on the canal bottom (concret material). Some physico- chemical characters were determined including conductivity ,salinity , pH, total alkalinity, total hardness, Ca ,Mg ,anddissolved oxygen. Water quality was fresh , alkaline, hard and well aerated.

This paper presents the dynamic responses of generators in a multi-machine power system.  The fundamental swing equations for a multi-machine stability analysis are revisited. The swing equations are solved to investigate the influence of a three-phase fault on the network largest load bus. The Nigerian 330kV transmission network was used as a test case for the study. The time domain simulation approach was explored to determine if the system could withstand a 3-phase fault. The stability of the transmission network is estimated considering the dynamic behaviour of the system under various contingency conditions. This study identifies Egbin, Benin, Olorunsogo, Akangba, Sakete, Omotosho and Oshogbo as the key buses w