We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

ABSTRACT Background: Cortical bone thickness is important for the stability of mini implants. Placing mini implants in sites of favorable cortical bone thickness would guarantee better initial stability and long-term success. The aim of this study was to investigate gender, side and jaw differences of the buccal cortical bone thickness as a guide for orthodontic mini screw placement. Materials and Methods: The sample was selected from the patients attending the Specialized Health Center in Al-Sadr City / 3D department. Thirty patients (15 males and 15 females) were selected and cone beam computerized tomographic images were done. Then the buccal cortical bone thickness was measured at thirteen inter radicular sites in the maxilla and mandib

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

In this search, a new pyrophosphate technique was proved. The technique was employed to single- nucleotide polymorphisms (SNPs), which diagnosis using a one-base extension reaction. Three Mycobacterium tuberculosis genes were chosen (Rpob, InhA, KatG) genes. Fifty-four specimens were used in this study fifty-three proved as drug-resistant specimens by The Iraqi Institute of Chest and Respiratory Diseases in Baghdad.; also one specimen was used as a negative control. The steps of this technique were by used a specific primer within each aliquot that has a short 3-OH end of the base of the target gene that was hybridized to the single-stranded DNA template. Then, the Taq polymerase enzyme and one of either α-thio-dATP, dTTP, dGTP, or dCTP