On a Closed Subspace of L^(p(.)(Ω))

In this study, we first give a description of L^(p(.)(Ω)) spaces. These spaces are an important generalization of classical Lebesgue spaces. We mention their various applications in engineering and physics fields. Thereafter, as it is naturally, one of the main task in L^(p(.)(Ω)) spaces is to generalize known properties classical Lebesgue spaces L^p(Ω)) to L^(p(.)(Ω)) spaces. Provided that measure of the set Ω is finite, we extend a theorem which about a closed subspace of space, from constant exponent to variable exponent. Our proof method based on embedding between L^(p(.)(Ω)) - L^p(Ω)) spaces and the proof of constant case. The essence of the method is to take advantage of properties of Hilbert space L^2(Ω)), and also based on the use of the closed graph theorem and finite measure of the set Ω.

Anahtar Kelimeler:

Variable Exponent, Lebesgue Space, Closed Subspace

The Synthesis, Characterization and Molecular Docking Studies of Novel 1,2,3-Triazole Derivatives as Xanthine Oxidase Inhibitor

In this study, the synthesis, characterization of novel 1,2,3-triazole compounds (4 and 5), investigation of their in vitro inhibition effects on xanthine oxidase and molecular docking studies were carried out. For this purpose, firstly; the target products (4 and 5) were synthesized by various chemical transformations starting from butadiene sulfone. All of the synthesized compounds were characterized by spectroscopic methods. In the second step; in vitro inhibition effects of compounds 4 and 5 on xanthine oxidase were investigated. According to the enzyme inhibition results, It was determined that compounds 4 (IC50 = 0.609 µM) and 5 (IC50 = 0.901 µM) showed stronger inhibition effect than allopurinol (IC50 = 1.143 µM), which is used as a drug for inhibition of xanthine oxidase. Finally, the binding modes of compounds 4 and 5 in the active part of xanthine oxidase (PDB ID:3NVY) were explained by molecular docking studies.

Keywords:

1, 2, 3-triazole, Xanthine oxidase 1, 3-dipolar cycloaddition, Molecular docking,

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