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The largest class of hyperstructures is the one which satisfies the weak properties and they are called H v-structures. In this paper, the concept of H v-S-act is introduced and some of their properties are investigated. The present paper establishes a possible connection between S-act, GHS-act and H v-S-act. It is shown that the quotient of GHS-act with any equivalence relation is H v-S-act. The main tool to study all hyperstructures is the fundamental relations. The study of fundamental relations in H v-S-act reveals some interesting results. Specifically, these relations connect weak hyperactions with the corresponding classical actions.

In this paper, we introduce the notion of generalized hyperaction of hypermonoid (GHS-act) on a set, establish its basic properties and prove some fundamental results. We also define the notion of prime, semiprime, irreducible and maximal GHS-subacts and characterize hypermonoid in terms of these GHS-subacts.

So far nuclear-armed states failed to create a global security framework that could improve global security and reduce the role of nuclear threat in relations between nuclear-armed states. All nine nuclear-armed states are engaged in nuclear weapons development and modernization aiming at diversity, precision, rapid mobilization and survivability, thereby increasing the probability of swift crisis escalation between nuclear-armed adversaries endangering the security of entire international community. Amid this weapons development and modernization, lack of and weak lines of communication between nuclear-armed adversaries during crises is crucial to work on as this could bring the world perilously close to sailing directly into the headwinds of nuclear war. The importance of building and maintaining communication between nucleararmed states during crises is indisputable. Hence, building an information flow via a backup hotline among supreme nuclear commanders based on agreed standard operating procedures (SOPs) for its operation could serve to reduce nuclear risk should it ever be needed. This hotline will socialize nuclear commanders and national leaders to be ready to: 1) disentangle communication during crises from domestic political pressures by practicing agreed SOPs of hotline before a crisis occurs, 2) build confidence among nuclear-armed states -and the international system in generalthat the means to control escalation exists, even if the political will is lagging, and 3) open opportunities for nuclear-armed states to broaden their discussion from the specifics of a nuclear hotline to the need to develop new norms that cover the entire nuclear command-and-control system.

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