In this work, we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied; j = , δ, α, pre, b, β

The aim of the present work is to synthesis of new 9-ethyl carbazole derivatives .The 3-acetyl-9-ethyl carbazole was achieved by the reaction of compound (1) with acetyl chloride in the presence of aluminum chloride to give compound (2). Reaction of compound (2) with a ppropriate aromatic aldehyde yielded 3-(3-Phenyl -1-Oxy propen-1-yl)9-Ethyl carbazole(3a-3h).The reaction of (3) with hydrazine hydrate gave 3-(5-aryl-4, 5-Dihydro-3-pyrozolyl)9-Ethyl carbazole(4a-4h). Also compound (3) reacted with phenyl hydrazine gave 3-(1-phenyl-5-aryl-4-pyrozoline-3-yl)9-Ethyl carbazole (5a-5h). The reaction of compound (3) with guanidine carbonate in presence of NaOH (40%) gave the 3-(2-amino-6-aryl-4-pyrimidinyl)9-Ethyl carbazole (6a-6h). The prepar

Phenoxathiin was prepared by the reaction of diphenyl ether with sulfur in the presence of anhydrous aluminum chloride. This work comprised the synthesis of new phenoxathiin derivatives containing heterocyclic moieties. These heterocyclic compounds were synthesized in three groups. The first group was made up of 2-(oxoalken-1-yl) phenoxathiin derivatives (3a-3j) obtained from the reaction of 2-acetylphenoxathiin with different aromatic aldehyde in the presence of sodium hydroxide. The other two groups involved compounds produced from the reaction of (3a-3j) with hydrazine hydrate in acetic acid to get 2-(1-acetyl pyrazolin-3-yl) phenoxathiin derivatives (4a-4j), and phenyl hydrazine in the presence of piperidine to afford 2-(1-phenyl pyrazo

Simplification of new fashion design methods

      In this article, we introduce a new type of soft spaces namely, soft  spaces as   a generalization of soft paces. Also, we study the weak forms of soft  spaces, namely, soft  spaces, soft  spaces, soft  space, and soft  spaces. The characterizations and fundamental properties related to these types of soft spaces and the relationships among them are also discussed.

     In this work, we introduce  a new convergence formula. We also define cluster point , δ-Cauchy sequence, δ-convergent, δ-completeness , and define sequentially contraction  in approach space. In addition, we prove the contraction condition is necessary and sufficient to get the  function is sequentially contraction  as well as we put a new structure for the norm in the approach space which is called approach –Banach space, we discuss the normed approach space with uniform condition is a Hausdorff space. Also, we prove a normed approach space is complete if and only if the metric generated from approach space is complete as well as prove every finite –dimensional approach normed space is δ-complete. We prove several r

Many of the elementary transformations of determinants which are used in their evaluation and in the solution of linear equations may by expressed in the notation of matrices. In this paper, some new interesting formulas of special matrices are introduced and proved that the determinants of these special matrices have the values zero. All formulation has been coded in MATLAB 7.