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.

Polymer films of PEG and PVA and their blend with different
concentrations of MnCl2 (0, 2, 4, 6 and 10 %.wt) were study using
casting technique. The X-ray spectra of pure PEG, PVA and
PVA:PEG films and with addition of 2% concentrations from
(MnCl2) show amorphous structures. The results for FTIR show the
interaction between the filler and polymer blend results in
decreasing crystallinity with rich amorphous phase. This
amorphous nature confirms the complexation between the filler and
the polymer blend. The optical properties of (PVA:PEG/MnCl2)
contain the recording of absorbance (A) and explain that the
absorption coefficient (α), refractive index (n), extinction coefficient
(ko) and the dielectric cons

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.

Iraq faces significant economic challenges, owing in part to its reliance on oil revenue and the country's overburdened public sector. The supremacy of State-Owned Enterprises (SOEs), obstructive rules, a lack of access to finance, a shortage of skilled labor, and inadequate infrastructure all impede private sector growth. This research relied mainly on information from global development organizations, most markedly the World Bank, as well as policy documents, and it discovered a scarcity of pertinent educational writings. The following are the key findings of this research: Recent economic growth has not resulted in poverty reduction; the stretched history of war and insecurity in Iraq has hampered progress and development; the private se

The problem motivation of this work deals with how to control the network overhead and reduce the network latency that may cause many unwanted loops resulting from using standard routing. This work proposes three different wireless routing protocols which they are originally using some advantages for famous wireless ad-hoc routing protocols such as dynamic source routing (DSR), optimized link state routing (OLSR), destination sequenced distance vector (DSDV) and zone routing protocol (ZRP). The first proposed routing protocol is presented an enhanced destination sequenced distance vector (E-DSDV) routing protocol, while the second proposed routing protocol is designed based on using the advantages of DSDV and ZRP and we named it as