the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

in this short note, we have given a short proof for the existence of the haar measure on commutative locally compact hypergroups based on functional analysis methods by using markov-kakutani fixed point theorem.

in a contract of carriage, parties have a right which arising out of the contract to give orders to carrier about  stopping goods in transit, delivering the goods to a person other than the consignee shown in the consignment note and etc.this right mostly belong to consigner but sometimes it’s transferred to consignee. it’s possible for the consignee when an entry to this effect made in the con...