The problem of finding the cyclic decomposition (c.d.) for the groups ), where  prime upper than 9 is determined in this work. Also, we compute the Artin characters (A.ch.) and Artin indicator (A.ind.) for the same groups, we obtain that after computing the conjugacy classes, cyclic subgroups, the ordinary character table (o.ch.ta.) and the rational valued character table for each group.

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is a basic pri

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

The orbital motion and longitude for some Jupiter's satellites (Amaletha, Europa, Ganymede and Callisto) were calculated from two different locations Iraq and Syria. A program was designed, the input parameters were the desired year, month, day and the longitude of the location, the output parameters results were applied in form of a file, and this file includes the longitude, orbital motion, and local time of these satellites. A specific date 1-10-2013 was taken, the results of longitude was (20-336) º and orbital motion was (92-331) º for both Iraq and Syria location with observing time (05:24:14-15:18:10) for Iraq and (04:56:33-14:50:30) for Syria. The difference in time between the two locations was constant (00:45:00), these results

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though