in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

In this paper, a new version of mean value theorem for interval-valued functions on time scales is established. Meantime, some basic concepts and results associated with semigroups operators are presented. As an application operators, under certain conditions, we consider the initial problem differential equations scales. Finally, two issues worthy further discussion

Grafting of glucosamine hydrochloride moieties to tetraphenylethylene (TPE) motif furnished a novel cationic water-soluble tetraphenylethylene derivative (GH-TPE). With aggregation-induced emission properties, GH-TPE was used for fluorometric detection to alkaline phosphatase through enzyme-triggered de-aggregation of the ensemble of GH-TPE and substrate.

We show that the nth derivative of Riemann zeta function, when summed over non-trivial zeros zeta, is real and positive/negative in mean for n odd/even, respectively. this by giving a full asymptotic expansion these sums.