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.

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.

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.

substitution is considered a method of meaning enrichment and is a formal substitution for the letter or the word inside the text, and it is an expression substitution that is a replacement of an element of a text with a formal or graphic element, and a substitution of a latter form by a previous vocalization, thus it results in a cohesive expression. Replacement inside the text happens through the existing relation between the word or the letter and the form within the phenomenon that is based on enhancing the meaning in a way that delimits the context. There are many studies and researches written about replacement, especially in the textual linguistics that focused on the literary and linguistic texts. Hence, the researcher found that

Theligand4-[5-(2-hydoxy-phenyl)- [1,3,4- thiadiazole-2- ylimino methyl]-1,5-dimethyl -2-phenyl-1,2-dihydro-pyrazol-3-one [HL1] is prepared and characterized. It is reacted with poly(vinyl chloride) (PVC) in THF to form the PVC-L compounds ,PVC-L interacted with ions of transition metals to form PVC-L-MII complexes .All prepared compounds are characterized by FTIR spectroscopy, u.v-visible spectroscopy, C.H.N.S. analysis and some of them by 1HNMR

Until The Second Half Of Nineteenth Century  , Psychology Depended On Philosophy In Its Experiences Which Means It Depend On Individuals Feelings Toward Psychological Experiences And Rapid Observation . As For The Scientific Organized Experimentation And Observation By Machines Have Been Used Later   .

The Experimentation Looking For The Cause Of  Phenomena And How Is That Happened   Also Reveal The Causal Relationship Between Among Phenomena . The Experiences In Psychology Field Include In Its Simplest Form Only One Variable ( Effective) Which Is Called Independent Variable As Well As Another Variable ( Affected )   That Called  Dependent Variable .