This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given. As the first result, it has been proved that every σ-algebra over a fuzzy set x* is a fuzzy σ-ring-over a fuzzy set x* and construct their converse by example. Furthermore, the fuzzy ring concept has been studied to generalize fuzzy algebra and its relation. Investigating that the concept of fuzzy σ-Ring is a stronger form of a fuzzy ring that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied as well. Finally, the main goal of this paper is to study these concepts and give basic properties, examples, characterizations and relationships between them.
This work involves synthesis of amides containing isoxazoline unit starting with
chalcone; 4-[3-(3‾-nitrophenyl)-2-propene- 1-one]-aniline[I]. 4-Aminoacetophenone was
reacted with 3-nitrobenzaldehyde in basic medium giving chalcone [I] by claisen-schemidt
reaction. The chalcone [I] was reacted with hydroxylamine hydrochloride giving isoxazoline
[II] in NaOH basic medium. The amides with structural formula [III]a-h were prepared by the
reaction of amino compounds ; isoxazoline [II] with different acid chlorides in dry pyridine
and using DMF as a solvent at 4
0
C. All the synthesized compounds have been characterized
by melting points , FTIR and
1
HMNR (of compound [III]a) spectroscopy.
Many new heterocyclic compounds including 4-thiazolidinones containing indole with triazole units were described. The new Schiff bases [VII]a, b and [VIII]a,b synthesized by condensation acid hydrazides [II],[VI] with different (aromatic) aldehydes in absolute ethanol. The refluxing equimolar amounts of the Schiff bases ([VII]a,b, [VIII]a,b) with thioglycolic acid in benzene led to get thiazolidin-4-ones derivatives ([IX]a,b and [X]a-d). Finally, the new derivatives [XI]a-c run out via the reacted compound [IX]a with di
Many new heterocyclic compounds including 4-thiazolidinones containing indole with triazole units were described. The new Schiff bases [VII] a, b and [VIII] a, b synthesized by condensation acid hydrazides [II],[VI] with different (aromatic) aldehydes in absolute ethanol. The refluxing equimolar amounts of the Schiff bases ([VII] a, b,[VIII] a, b) with thioglycolic acid in benzene led to get thiazolidin-4-ones derivatives ([IX] a, b and [X] ad). Finally, the new derivatives [XI] ac run out via the reacted compound [IX] a with different n-alkyl bromide (methyl bromide, ethyl bromide, and butyl bromide)
This work involves synthesis and characterization of some new 1, 3, 4-thiadiazole or pyrazoline derivatives heterocyclic containing indole ring. The new 2-amino-1, 3, 4-thiadiazole derivatives [IV] and [V] a, b were synthesized by cyclization reaction of 2-methyl-1H-indole-carbothiosemicarbazide [III] in H2SO4 acid or by reaction of indole-3-acetic acid or indole-3-butanoic acid with thiosemicarbazide in the presence of phosphorous oxychloride, respectively. Amide derivatives [VI]-[VIII] were synthesized by the reaction equimolar of 2-amino-1, 3, 4-thiadiazoles and (acetyl chloride, benzoyl chloride, anisoyl chloride and heptanoyl chloride) in DMF and pyridine as accepter. The new pyrazolone derivatives [XI] a, b were synthesized from heati
... Show MoreThis work involves synthesis and characterization of some new 1, 3, 4-thiadiazole or pyrazoline derivatives heterocyclic containing indole ring. The new 2-amino-1, 3, 4thiadiazole derivatives[IV] and [V]a, b were synthesized by cyclization reaction of 2-methyl1H-indole-carbothiosemicarbazide[III] in H2SO4 acid or by reaction of indole-3-acetic acid or indole-3-butanoic acid with thiosemicarbazide in the presence of phosphorous oxychloride, respectively. Amide derivatives [VI]-[VIII] were synthesized by the reaction equimolar of 2amino-1, 3, 4-thiadiazoles and (acetyl chloride, benzoyl chloride, anisoyl chloride and heptanoyl chloride) in DMF and pyridine as accepter. The new pyrazolone derivatives [XI]a, b were s
... Show MoreIn this work 5-methylene-yl - (2-methy –oxazole-4-one) (1H) imidazole (1) were synthesized from the reaction of L-Histidine with acetic anhydride and which converted to the of 5-methylene-yl-(2-methyl 3-amino imidazole-4-one)-1H-imidazole (2) by reaction with hydrazine hydrate. Schiff bases (3-6) were synthesized from the reaction of compound (2) with different aromatic aldehyde. Reaction of compounds (3-6) with chloroacetyl chloride gives azetidinone one derivatives (7-10). These compounds were characterized by FT-IR and some of them with 1H-NMR and 13C-NMR spectroscopy.
Let R be a Г-ring, and σ, τ be two automorphisms of R. An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]α = [a,b]α(σ,τ) holds for all a,b∈R and α∈Γ. In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-ring.
This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor
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Condensation of 4-methoxybenzoyl hydrazine with 4- aminobenzoic acid in the presence of POCl3 gave the oxadiazole derivative [III] .This compound was demethylated with aluminium chloride to give series of 2- (4-hydroxy phenyl)-5-(4-amino phenyl)
1,3,4-oxadiazole [IV]. Series of Schiff s bases [V]n were synthesized by the condensation of compound [IV] with 4-n-alkoxy benzaldehyde in the presence of glacial acetic acid. Condensation of compounds [VI]n. with adipoyl chloride in dry pyridine leads to the formation of a new homologous series [VI]n. The structures of the synthesized compounds were confirmed by physical and spectral means The new compounds [VI]n have been screened for their antibacterial activities . The results