We consider how selfish agents are likely to share revenues derived from maintaining connectivity between important network servers. We model a network where a failure of one node may disrupt communication between other nodes as a cooperative game called the vertex Connectivity Game (CG). In this game, each agent owns a vertex, and controls all the edges going to and from that vertex. A coaliti...

This work presents the utilization of amphiphilic poly(oligo(ethylene glycol) methyl methacrylate)-co-poly(2-(diisopropylamino)ethyl methacrylate), P(OEGMA-co-DIPAEMA), hyperbranched (HB) copolymers, forming polymeric aggregates in aqueous media, as building nanocomponents and nanocarriers for entrapment magnetic cobalt ferrite nanoparticles (CoFe2O4, MNPs), hydrophobic drug curcumin (CUR) thei...

The Ehrenfeucht-Fraı̈ssé method for first-order logic and further logics relevant in descriptive complexity has been quite successful. However, for key problems such as P 6= NP or NP 6= co-NP no progress has been achieved using it. We show that for these problems we can not get the board for the corresponding Ehrenfeucht-Fraı̈ssé game in polynomial output time, even if we allow probabilistic meth...

In this work we continue the syntactic study of completeness that began with the works of Immerman and Medina. In particular, we take a conjecture raised by Medina in his dissertation that says if a conjunction of a second-order and a first-order sentences defines an NP-complete problems via fops, then it must be the case that the secondorder conjoint alone also defines a NP-complete problem. A...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

Suppose X is the complex zero set of a finite collection of polynomials in Z[x1, ..., xn]. We show that deciding whether X contains a point all of whose coordinates are dth roots of unity can be done within NP (relative to the sparse encoding), under a plausible assumption on primes in arithmetic progression. In particular, our hypothesis can still hold even under certain failures of the Genera...

in this paper, we introduce the notion of primal strong co-ideals and give some results involving them. it is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.