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.

This study is about the role of the Internet in spreading rumors, especially through social networking sites "Facebook" model as the effectiveness of social networks lies in the speed of transmission of events; these two characteristics are important to the public, making the Internet a strong contender for television and its relationship with the public. That's why we find that the Internet today has become a fertile environment for the growth and spread of rumors. The more limited the platforms and places of publication, the greater the responsibility in the search for the original source in   spreading this or that rumor, as the Internet is considered an easy means in the production, spreading  and re-spreading  of

The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

The new tridentate Schiff base ligand (HL)namely 2-{[1-(3-amino-phenyl)-ethylidene]-hydrazono methyl}- phenol containing (N N O)as donors atoms was prepared in two steps:Step (1): By the reaction of 3- aminoacetophenone with hydrazine monohydrate under reflux in methanol and drops of glacial acetic acid gave the intermediate compound 3-(1- hydrazono ethyl)-phenol amine.Step (2): By the reaction of 3-(1-hydrazono ethyl)-phenol amine with salicyaldehyde under reflux in methanol, gave the ligand (HL).The prepared ligand was characterized by I.R, U.V-Vis,1H- 13C NMR spectra and melting point and reacted with some metal ions under reflux in methanol with (1:1) ratio gave complexes of the general formula: [MClL]. Where: M= Mn(II), Fe(II), Co(II),

The syntheses, characterizations and structures of three novel dichloro(bis{2-[1-(4-methoxyphenyl)-1H-1,2,3-triazol-4-yl-κN3]pyridine-κN})metal(II), [M(L)2Cl2], complexes (metal = Mn, Co and Ni) are presented. In the solid state the molecules are arranged in infinite hydrogen-bonded 3D supramolecular structures, further stabilized by weak intermolecular π…π interactions. The DFT results for all the different spin states and isomers of dichloro(bis{2-[1-phenyl-1H-1,2,3-triazol-4-yl-κN3]pyridine-κN})metal(II) complexes, [M(L1)2Cl2], support experimental measurements, namely that (i) d5 [Mn(L1)2Cl2] is high spin with S = 5/2; (ii) d7 [Co(L1)2Cl2] has a spin state of S = 3/2, (iii) d8 [Ni(L1)2Cl2] has a spin state of S =

New series of 4,4'-((2-(Aryl)-1H-benzo[d]imidazole1,3(2H)-diyl)bis(methylene))Diphenol(3a-g) was successfully synthesized from cyclization of the reduction product of bis Schiff bases (2) with aryl aldehydes bearing phenolic hydroxyl in the presence of acetic acid. The structure of these compounds was identified from FT-IR, 1H NMR, 13C NMR and EIMs. The Antioxidant capability was screened by DPPH and FRAP assays. Both assays showed antioxidant capability more than BHT as well. Compounds 3b and 3c showed antioxidant capacity slightly less than ascorbic acid. The docking study for theses compound was carried out as III DNA polymerase inhibitor. The results of docking demonstrated that the increase in hinderances around phenolic hy

New series of 4, 4'-((2-(Aryl)-1H-benzo [d] imidazole-1, 3 (2H)-diyl) bis (methylene)) Diphenol (3a-g) was successfully synthesized from cyclization of the reduction product of bis Schiff bases (2) with aryl aldehydes bearing phenolic hydroxyl in the presence of acetic acid. The structure of these compounds was identified from FT-IR, 1H NMR, 13C NMR and EIMs. The Antioxidant capability was screened by DPPH and FRAP assays. Both assays showed antioxidant capability more than BHT as well. Compounds 3b and 3c showed antioxidant capacity slightly less than ascorbic acid. The docking study for theses compound was carried out as III DNA polymerase inhibitor. The results of docking demonstrated that the increase in hinderances around phenolic hydr

     Bimetallic Au –Pt catalysts supporting TiO₂ were synthesised using two methods; sol immobilization and impregnation methods. The prepared catalyst underwent a thermal treatment process at 400^◦ C, while the reduction reaction under the same condition was done and the obtained catalysts were identified with transmission electron microscopy (TEM) and energy-dispersive spectroscopy (EDS). It has been found that the prepared catalysts have a dimension around 2.5 nm and the particles have uniform orders leading to high dispersion of platinum molecules .The prepared catalysts have been examined as efficient photocatalysts to degrade the Crystal violet dye under UV-light. The optimum values of Bimetallic Au –

In this research we assumed that the number of emissions by time (𝑡) of radiation particles is distributed poisson distribution with parameter (𝑡), where  < 0 is the intensity of radiation. We conclude that the time of the first emission is distributed exponentially with parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃 ∗ for 𝜃 is more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived variances of both estimators as a statistical indicator for efficiency

Novel derivatives of 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole and 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole carrying Schiff bases moiety were synthesised and fully characterised. The protection of D- fructose using benzoyl chloride was synthesized, followed by nucleophilic addition/elimination between benzotria- zole and chloroacetyl chloride to give 1-(1- chloroacetyl)- 1H-benzotriazole. The next step was condensation reaction of protected fructose and 1-(1-chloroacetyl)-1H- benzotriazole producing a new nucleoside analogue. The novel nucleoside analogues underwent a second conden- sation reaction with different aromatic and aliphatic amines to provide new Schiff b