Let  be a Banach algebra and  a derivation. In this paper, it is proved, under certain conditions, that , where  is the Jacobson radical of . Moreover, we prove that if  is unital and  is a continuous derivation, then , ...

Let S be a monoid and X a class of S-acts which is closed under coproducts. The object of this article is to find conditions under which all S-acts have X-precovering. We have shown that the existence of torsion-free ...

In this paper we introduce entire sequence spaces defined by a sequence of modulus functions . We study some topological properties of these spaces and prove some inclusion relations.

Titanium dioxide nanocrystals were synthesized by sol-gel method at room temperature. Titanium isoprophoxide and absolute ethanol were used as precursors to prepare the sol. The pH of the solution was adjusted by adding ...

The mobility and bioavailability of trace elements in the agricultural soils are extremely important in assessing the risk of toxicity to the growing plants. A five step sequential extraction procedure (SEP) has been ...

In this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( -derivations in -algebras. We introduce ...

Dodecylbenzenesulfonic acid (DBSA) was used as an efficient, cheap and stable Brønsted catalyst for acetylation of alcohols and phenols and formylation of alcohols under solvent-free conditions. Various primary, secondary ...