A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

Today, urban Stormwater management is one of the main concerns of municipalities and stakeholders. Drought and water scarcity made rainwater harvesting one of the main steps toward climate change adaptation. Due to the deterioration of the quality of urban runoff and the increase of impermeable urban land use, the treatment of urban runoff is essential. Best Management Practice (BMP) and Low Impact Development (LID) approaches are necessary to combat climate change consequences by improving the quantity and quality of water resources. The application of Bioswales along urban streets and roadways can reduce the stress on water resources, recharge groundwater and prevent groundwater pollution. While Sulaymaniyah City has a

In this paper a dynamic behavior and control of  a jacketed continuous stirred tank reactor (CSTR)  is developed using different control strategies, conventional feedback control (PI and PID), and neural network (NARMA-L2, and NN Predictive) control. The dynamic model for CSTR process is described by a first order lag system with dead time.

The optimum tuning of control parameters are found by two different methods; Frequency Analysis Curve method (Bode diagram) and Process Reaction Curve using the mean of Square Error (MSE) method. It is found that the Process Reaction Curve method is better than the Frequency Analysis Curve method and PID feedback controller is better than PI feedback controller.

The results s

Background: Langerhans' cell histiocytosis (LCH) is a group of conditions affecting the reticuloendothelial system. It includes Letterer-Siwe disease, Hand-Schuller-Christian disease and eosinophilic granuloma and most often presents in childhood. Materials and methods: Twenty-five cases of LCH were diagnosed histologically and confirmed by CD1a antibody and assessed immunohistochemically using anti-RANKL and anti-RANK antibodies to evaluate osteoclastogenic mechanism. Results: Regarding jaw cases, there was a significant correlation between CD1a and RANK (P=0.016). While in the skull, highly significant correlation existed between RANK and RANKL (p=0.001). Among the sites, there was no statistically significant difference found for each

Numerical study is adapted to combine between piezoelectric fan as a turbulent air flow generator and perforated finned heat sinks. A single piezoelectric fan with different tip amplitudes placed eccentrically at the duct entrance. The problem of solid and perforated finned heat sinks is solved and analyzed numerically by using Ansys 17.2 fluent, and solving three dimensional energy and Navier–Stokes equations that set with RNG based k−ε scalable wall function turbulent model. Finite volume algorithm is used to solve both phases of solid and fluid. Calculations are done for three values of piezoelectric fan amplitudes 25 mm, 30 mm, and 40 mm, respectively. Results of this numerical study are compared with previous b