Weighted ebyev-Ostrowski type inequalities

In account of the famous ebyev inequality,a rich theory has appeared in the literature.We establish some new weighted ebyev type integral inequalitíes.Our proofs are of independent interest and provide new estimates on these types of inequalities.     

N-Phenacyldibromobenzimidazoles—Synthesis Optimization and Evaluation of Their Cytotoxic Activity

Antifungal N-phenacyl derivatives of 4,6- and 5,6-dibromobenzimidazoles are interesting substrates in the synthesis of new antimycotics. Unfortunately, their application is limited by the low synthesis yields and time-consuming separation procedure. In this paper, we present the optimization of the synthesis conditions and purification methods of N-phenacyldibromobenzimidazoles. The reactions were carried out in various base solvent-systems including K₂CO₃, NaH, KOH, t-BuOK, MeONa, NaHCO₃, Et₃N, Cs₂CO₃, DBU, DIPEA, or DABCO as a base, and MeCN, DMF, THF, DMSO, or dioxane as a solvent. The progress of the reaction was monitored using HPLC analysis. The best results were reached when the reactions were carried out in an NaHCO₃–MeCN system at reflux for 24 h. Additionally, the cytotoxic activity of the synthesized compounds against MCF-7 (breast adenocarcinoma), A-549 (lung adenocarcinoma), CCRF-CEM (acute lymphoblastic leukemia), and MRC-5 (normal lung fibroblasts) was evaluated. We observed that the studied cell lines differed in sensitivity to the tested compounds with MCF-7 cells being the most sensitive, while A-549 cells were the least sensitive. Moreover, the cytotoxicity of the tested derivatives towards CCRF-CEM cells increased with the number of chlorine or fluorine substituents. Furthermore, some of the active compounds, i.e., 2-(5,6-dibromo-1H-benzimidazol-1-yl)-1-(3,4-dichlorophenyl)ethanone (4f), 2-(4,6-dibromo-1H-benzimidazol-1-yl)-1-(2,4,6-trichlorophenyl)ethanone (5g), and 2-(4,6-dibromo-1H-benzimidazol-1-yl)-1-(2,4,6-trifluorophenyl)ethanone (5j) demonstrated pro-apoptotic properties against leukemic cells with derivative 5g being the most effective.