In this work,   polynomials  and the finite q-exponential operator  are constructed. The operator  is used to combine an operator proof of the generating function with its extension, Mehler's formula with its extension and Roger's formula for the polynomials . The generating function with its extension,  Mehler's formula with its extension and Rogers formula for Al-Salam-Carlitz polynomials  are deduced by giving special values to polynomials .

New 1,3-oxazol-5(4H)-one(3) was synthesized by cyclization of[(4-Methyl phenyl-carbonyl)amino]acetic acid (2). The starting materials were readily obtained by acylation of 2-amino acetic acid (Glycine) with 4-methyl phenyl chloride .Imidazole(4) was synthesized by reaction of compound (3) with hydrazine hydrate (99%). Compound (4) was isolated and characterized by 1HNMR , FTIR , uv-vis spectroscopy and elemental analysis (C.H.N). Compound (4) has been used as a ligand (L) to prepare a number of metal complexes with Cr(III), Mn(II), Co(II), Ni(II) , Cu(II) and Zn(II).
The prepared complexes were isolated and characterized by FTIR and Uv-vis spectroscopy elemental analysis (C.H.N), flame atomic absorption technique, as well as magnetic

     Synthesis of new heterocyclic compounds containing four five-membered rings together was the main goal of this work. The new derivatives of [tetrakis (1,2,4-triazole /1,3,4-thiadiazole /1,3,4-oxadiazole][bis-(benzene-1,3,5-triyl)] dioxymethylene A7-A18 were synthesized by the reaction of [bis-(dimethyl 5-yl-isophthalate)] dioxymethylene compound A1 which was previously prepared from the reaction of 1,2-dibromomethan and dimethyl 5-hydroxyisophthalate, then treated with hydrazine hydrate to yield the corresponding acid hydrazide A2. In the next step, compound A2 was refluxed with 4-substituted isothiocyanate to give substituted thiosemicarbazides A3-A6. The treatment of the latter compounds in basic medium of 2M o

    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

The Co (II), Ni (II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II) complexes of mixed of amino acid (L-Alanine ) and Trimethoprim antibiotic were synthesized. The complexes were characterized using melting point, conductivity measurement and determination the percentage of the metal in the complexes by flame (AAS). Magnetic susceptibility, Spectroscopic Method [FTIR and UV-Vis]. The general formula have been given for the prepared mixed ligand complexes [M(Ala)2(TMP)(H2O)] where L- alanine (abbreviated as (Ala ) = (C5H9NO2) deprotonated primary ligand, L- Alanine ion .= (C5H8NO2 -) Trimethoprim (abbreviated as (TMP ) = C10H11N3O3S M(II) = Co (II),Ni(II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II). The results showed that the deprotonated L- Alanine by KOH (Ala

 The paper tackles two topics. The first is about the term "Ремейк" which is very common in contemporary Russian literature; it has counterparts such as " Обработка" and " Переделка", where these two may indicate any of the following meanings (remake, reformulate, rewrite, treatment, modification, change). It has been shown that this term does not have a stable definition. Also, the role of this term in literary studies has been mentioned along with how it has come to its peak of use in post-modern literature.

The second is that I have taken a sample of well-known works in Russian literature " On the Eve, On the Eve " by the contemporary Russian writer YevgueniBobov, and shown the effort of the writer

The adsorption ability of Iraqi initiated calcined granulated montmorillonite to adsorb Symmetrical Schiff Base Ligand 4,4’-[hydrazine-1, 2-diylidenebis (methan-1-yl-1-ylidene)) bis (2-methoxyphenol)] derived from condensation reaction of hydrazine hydrate and 4-hydroxy-3-methoxybenzaldehyde, from aqueous solutions has been investigated through columnar method.The ligand (H2L) adsorption found to be dependent on adsorbent dosage, initial concentration and contact time.All columnar experiments were carried out at three different pH values (5.5, 7and 8) using buffer solutions at flow rate of (3 drops/ min.),at room temperature (25±2)°C. The experimental isotherm data were analyzed using Langmuir, Freundlich and Temkin equations. The monol