Abstract. In this work, some new concepts were introduced and the relationship between them was studied. These concepts are filter directed-toward, nano-closure-directed-toward and nano-closure-converge to point, and some theories and results about these concepts were presented. A definition almost-nano-converges for set, almost-nano-cluster-point, and definition of quasi-nano-Hausdorff-closed and was also called nano-Hausdorff-closed relative, were also presented several theories related to these definitions were presented and the relationship between them was studied . We also provided other generalizations, including nano closure continuous mappings and it was also called as nano-weaklycontinuous- mappings, as well as providing a definit

We introduce some new generalizations of some definitions which are, supra closure converge to a point, supra closure directed toward a set, almost supra converges to a set, almost supra cluster point, a set supra H-closed relative, supra closure continuous functions, supra weakly continuous functions, supra compact functions, supra rigid a set, almost supra closed functions and supra perfect functions. And we state and prove several results concerning it

In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.

In this study, new heterocyclic compounds were synthesized through the cyclization reactions of o-phenylenediamine (1) with various organic reagents. Benzodiazepine derivatives (2-4) were obtained by reaction of (1) with ethylacetoacetate, malonic acid and acetyl acetone.Treatment of compound (1) with chloroacetamide, chloroacetic acid, p-bromophenacyl bromide and oxalic acid dihydrate afforded quinoxaline derivatives (5-8), respectively. Reaction of compound (1) with benzoic acid, piperonal, cyclohexanone and carbon disulfide resulted in the formation of compounds (9-12), respectively. Finally, reaction of compound (12) with chloroacetic acid in the presence of potassium hydroxide produced compound (13).

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The mixed ligand complexes of Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) with alanine and 8-hydroxyqinoline (Oxine) were synthesized and characterized by FT-IR ,spectra electronic, flam-AAS] along with conductivity measurements , solubility , melting point, magnetic susceptipibility.The synthesized complexes were tested in vitro for antimicrobial activity. The results obtained indicated that some of these complexes are more active than with others.

We described herein the synthesized and characterized of new bent and liner core compounds containing thiazolidin-4-one ring[XI-XIII] and [XIV-XVI] respectively. These compounds synthesized by sequence reactions starting from reaction resorcinol or hydroquinone with chloracetyl chloride to yield compounds [I] and [II] ,then the later compounds reactant with 4-hydroxybenzylaldehyde to product dialdehyde compounds [III] and [IV] .The Schiff bases compounds[V-VII] and [VIII-X] synthesized from reaction the compound [III] or [IV] with different aromatic amines, while the bent and liner core mesogens containing thiazolidin-4-one ring [XI-XIII] and [XIV-XVI] synthesized from reaction Schiff bases compounds[V-VII] or [VIII-X] with thioglycolic aci