This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

This work involves synthesis of some new heterocyclic compounds including 1, 3-diazetine. The new Schiff bases [VI] ad derived from 3-((5-hydrazinyl-4-phenyl-4H-1, 2, 4-triazol-3-yl) methyl)-1H-indole [V] which was synthesized by refluxing 5-((1H-indol-3-yl) methyl)-4-phenyl-4H-1, 2, 4-triazole-3-thiol [IV] with hydrazine hydrate in absolute ethanol and this amino compound [V] condensation with different aromatic aldehydes in absolute ethanol to yielded a new Schiff bases [VI] ad. N-acyl compounds [VII] ad were synthesized by addition reaction of acetyl chloride to imine group of Schiff bases in dry benzene. The new diazetine derivatives [VIII] ad synthesized by the reaction of N-acyl compounds [VII] ad with sodium azide in dimethylformamid

The complexes of the 2-hydroxy-4-Nitro phenyl piperonalidene with metal ions Cr(III), Ni(II), Pt(IV) and Zn(II) were prepared in ethanolic solution. These complexes were characterized by spectroscopic methods, conductivity, metal analyses and magnetic moment measurements. The nature of the complexes formed in ethanolic solution was study following the molar ratio method. From the spectral studies, monomer structures proposed for the nickel (II) and Zinc (II) complexes while dimeric structures for the chromium (III) and platinum (IV) were proposed. Octahedral geometry was suggested for all prepared complexes except zinc (II) has tetrahedral geometry, Structural geometries of these compounds were also suggested in gas phase by using

   Ethylenediamine was reacted in the first step with 2,5 – hexandion to produce the precursor [A] , then [A] was reacted with diethylmalonate to give the new tetradentate macrocyclic Ligand [H2L].This Ligand was reacted with some metal ions in ethanol to give a series of new metal complexes of the general formula [M(HnL)X]m  ( where : M= CrIII  ,      n = 0 ,  X= Cl2 , m= -1 ;  M = MnII , FeII , NiII , CuII ,      n = 1 , X= Cl2 , m = -1 ;  M = CoII , n = 0 ,       X = Cl , m = -1 ; M = PdII , n = 0 , X=0 , m = 0  ; M = CdII , n = 2 , X = 0 ,     m = +2 .  All compounds were characterize

This work represents the preparation of the starting material, 3-chloro-2-oxo-1,4-dithiacyclohexane (S) using a new method. This material was reacted with, 4-phenylthiosemicarbazide to give (H3NS3) as a tetradentate ligand H3L. New complex of rhenium (V) with this ligand of the formula [ReO(L)] was prepared. New complexes of the general formula [M(HL)] of this ligand when reacted with some metal ions where: M = Ni(II), Cu(II), Cd(II), Zn(II), Hg(II) have been reported. The ligand and the complexes were characterized by infrared, ultraviolet–visible, mass, 1H nuclear magnetic resonance and atomic absorption spectroscopic techniques and by (HPLC), elemental analysis, and electrical conductivity. The proposed structure for H3L with Re (V) i

In this study new derivatives of O-[2-{''2-Substituted Aryl (''1,''3,''4 thia diazolyl) ['3,'4b]-'1,'2,'4- Triazolyl]-Ethyl]-p- chlorobenzald oxime (6-11) have been synthesized from the starting material p-chloro – E- benzaldoxime 1. Compound 2 was synthesized by the reaction of p-chloro – E- benzaldoxime with ethyl acrylate in basic medium. Refluxing compound 2 with hydrazine hydrate in ethanol absolute afforded 3. Derivative 4 was prepared by the reaction of 3 with carbon disulphide, treated of compound 4 with hydrazine hydrate gave 5. The derivatives (6-11) were prepared by the reaction of 5 with different substitutes of aromatic acids. The structures of these compounds were characterized from their melting points, infra

The reaction of 2-amino benzoic acid with 1,2-dichloroethane under reflux in methanol and KOH as a base to gave the precursor [H₄L]. The precursor under reflux and drops of CH₃COOH which reacted with (2mole) from salicycaldehyde in methanol to gave a new type N₂O₄ ligand [H₂L], this ligand was reacted with (MCl₂) Where [M= Co (II), Ni(II), Cu(II) and Zn(II)] in (1:1) ratio at reflux in methanol using KOH as a base, to give complexes of the general formula [M(L)]. All compounds have been characterized by spectroscopic methods [¹H NMR ( just to the ligand), FTIR, uv-vis, atomic absorption], melting point, conductivity, chloride content, as well as m

The reaction of 2-amino benzoic acid with 1,2-dichloroethane under reflux in methanol and KOH as a base to gave the precursor [H4L]. The precursor under reflux and drops of CH3COOH which reacted with (2mole) from salicycaldehyde in methanol to gave a new type N2O4 ligand [H2L], this ligand was reacted with (MCl2) Where [M= Co (II), Ni(II), Cu(II) and Zn(II)] in (1:1) ratio at reflux in methanol using KOH as a base, to give complexes of the general formula [M(L)]. All compounds have been characterized by spectroscopic methods [1H NMR ( just to the ligand), FTIR, uv-vis, atomic absorption], melting point, conductivity, chloride content, as well as magnetic susceptibility measurements. From the above data, the proposed molecular structu