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We consider the Euclidean topology and s−topology on n−dimensional Minkowski space and investigate the interior and closure of the space cone and perforated space cone with respect to these topologies. In these regards, we determine that whether the space cone and perforated space cone are generalized open set or not. Moreover, we compare the generalized Euclidean topologies with the generalized s−topologies.

Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z) = nP(z) + (α − z)P 0 (z) denote the polar derivative of P(z) with respect to a complex number α. In this paper, we present an integral inequality for the polar derivative of a polynomial P(z). Our result includes as special cases several interesting generalizations of some Zygmund type inequalities for polynomials.

Synthesis, characterization and biological evaluation of 1,3-thiazolidine-4-ones derived from (2S)-2-benzoylamino-3-methylbutanohydrazide hydrazones.

Objective: In traditional medicine, the Pulicaria species are used for various disorders such as inflamed wounds, skin diseases, and bronchitis. This study investigated the antibacterial effect of five Pulicaria species in Turkey; (Pulicaria (P) arabica (L.) Cass., P. dysenterica (L.) Bernh., P. odora (L.) Reichb., P. sicula (L.) Moris, P. vulgaris (L.) Gaertn.) against certain significant pathogenic gram-negative and gram-positive reference bacteria. Material and Method:Four extracts (decoction, infusion, aqueous, and ethanol (EtOH) extracts) were prepared from the Pulicaria species. The antimicrobial activity of the samples was examined against reference organisms; Bacillus (B) subtilis, Enterococcus faecalis, Escherichia coli, Klebsiella pneumoniae, Methicillin-resistant Staphylococcus (S) aureus (MRSA), Proteus mirabilis, S. aureus and Pseudomonas aeruginosa. The minimal bactericidal concentration (MBC) and minimum inhibitory concentration (MIC) ranges of the extract samples were demonstrated based on a microbroth dilution method. Results:The EtOH extracts of the studied four Pulicaria species were found to be weakly active against gram-positive bacteria such as B. subtilis, MRSA and S. aureus but the EtOH extract of P. dysenterica showed exceptionally good activity against the reference strains of S. aureus, MRSA. No antimicrobial activity was detected in the infusion, decoction, and aqueous extracts. Conclusion:The Pulicaria species, especially P. dysenterica could be evaluated as antimicrobial agents. Further studies with the extracts and essential oils from Pulicaria sp. on other bacteria and pathogenic fungi should be performed.