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.

Variable selection in Poisson regression with high dimensional data has been widely used in recent years. we proposed in this paper using a penalty function that depends on a function named a penalty. An Atan estimator was compared with Lasso and adaptive lasso. A simulation and application show that an Atan estimator has the advantage in the estimation of coefficient and variables selection.

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.

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.

Zora Neale Hurston's (1891-1960) is an outstanding African American
novelist, playwright, autobiographer and essayists. Her work is considered as an
important part of the African American and Harlem Literature.**** It represents a
milestone and a keystone in the African-American literary canon because it breaks
from the style of the previous works and makes a beginning of a new style. Hurston
shifts from the black works that stick to racial themes and sheds the light on new
aspects and themes in blacks' life especially on feminist themes. Her exceptional fame
culminates in her novel Their Eyes Were Watching God (1937). 1
Their Eyes Were Watching God examines with a great deal of artistry
the struggle of a black

The first chapter includes introduce the research and the problem of the research that there are negligence of some educational institutions and schools management  , some parents and supervisors .Also there are some educators who believes that school activities are obstacles means to learning and prevent pupils from studying and understanding the subjects. That may due to social , psychological and educational reasons

The purposes of the researches come from the reports of supervision visits which indicate a lot of difficulties faced by pupils and teachers related to education activities  and its influence on in education  and the necessity of indentify these difficulties and remedy them