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- Author or Editor: A. Keskin x
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Summary
We introduce the notion of a semi-I-regular set and investigate some of its properties. We show that it is weaker than the notion of a regular-I-closed set. Additionally, we also introduce the notion of an AB I -set by using the semi-I-regular set and study some of its properties. We conclude that a subset A of an ideal topological space (X,τ,I) is open if and only if it is an AB I -set and a pre-I-open set.
Abstract
First, we introduce the notion of f I-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of R I C-continuous, f I-continuous and contra*-continuous functions and we show that a function f: (X,τ,I) to (Y,ϕ) is R I C -continuous if and only if it is f I-continuous and contra*-continuous.
Summary In [6] we introduced and investigated the notions of f I -sets and f I -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.
Abstract
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,ϕ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A I-sets and A I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, ϕ) is continuous if and only if it is α-I-continuous and A I-continuous.
Abstract
We deal with the Dirac operator with eigenvalue dependent boundary and jump conditions. Properties of eigenvalues, eigenfunctions and the resolvent operator are studied. Moreover, uniqueness theorems of the inverse problem according to the Weyl functions and the spectral data (the sets of eigenvalues and norming constants; two different eigenvalues sets) are proved.
Honey is the most important bee product. There are many secondary metabolites, carbohydrates, enzymes, and vitamins in honey, thus, honey has antimicrobial activity. In this study, in vitro antimicrobial activity of forty-two honey and eight propolis ethanolic extracts (PEE) were investigated against 16 microorganisms. Total phenolic content ranged between 20.00–124.10 mg GAE/100 g and 103–232 mg GAE/g for honey and raw propolis samples, respectively. Pine and oak honeydew honeys had higher antimicrobial activity than four different grades of Manuka Honeys up to 18 mm minimum inhibition zone diameters. The ethanolic propolis extracts showed much higher antimicrobial activity than the honey samples. Fungi species were inhibited by the propolis samples. Helicobacter pylorii (H. pylorii) was the most sensitive, whereas Streptococcus agalactiae was the most resistant bacteria among the studied microorganisms. Brazilian and Zonguldak propolis had the closest antimicrobial activity to ampicillin, streptomycin, and fluconazole. It can be concluded that both honey and propolis could be used in preservative and complementary medicine.
