Abstract In this paper, we consider the problem of cross-chain payment whereby customers different escrows—implemented by a bank or blockchain smart contract—successfully transfer digital assets without trusting each other. Prior to work, problems did not require success, any form progress. We introduce new specification formalism called Asynchronous Networks Timed Automata formalise such proto...

Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.