This research aims at recognizing the concept of Innovation in offering the banking services as well as the concept and dimensions of competitive advantage . And to identify and analyze the relationship ( correlation and impact ) between the concept of Innovation in  offering the banking services and the dimensions of the competitive advantage under discussion . The research includes all Iraqi private banks in Baghdad city only of the (20) banks . The researcher adopted , in this study , a random sample of the distribution of the questionnaire to members of the research sample are managers , customers and employees in these banks , and were distributed ( 115 ) form  questionnaire , ( 97 ) form w

In this study, an efficient photocatalyst for dissociation of water was prepared and studied. The chromium oxide (Cr₂O₃) with Titanium dioxide (TiO₂) nanofibers (Cr₂O₃-TNFs) nanocomposite with (chitosan extract) were synthesized using ecologically friendly methods such as ultrasonic and hydrothermal techniques; such TiO₂ exhibits nanofibers (TNFs) shape struct

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.

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 necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

The article considers metaphors as one of the fundamental means used by L. Ulitskaya when writing the family chronicle "Medea and her Children" (1996), for the formation of images of heroines - representatives of the pronounced feminine principle in the work. Here I describe the results of the next stage of research related to the work of Lyudmila Evgenievna Ulitskaya as a representative of modern Russian prose.

<em>The aim of the research is to set a set of BioKinematic variables for the step of crossing barriers (3–6–9) in a 110-meter barrier for young runners. The researchers concluded the study by interpreting and discussing the results that the most important variables must be relied upon when training and selecting runners that got the best saturation on their factors: 1-The first factor which refers to the total distance of the plan to pass the third barrier + the total distance of the plan to pass the ninth barrier + the total distance Plan to cross the sixth barrier. 2-The second factor which refers to the total vertical speed before passing the third barrier + the total vertical speed before the sixth barrier + the total vertica