Given a real bounded sequence $x=(x_{j})$ and an infinite matrix $A=(a_{nj})$ Knopp core theorem is equivalent to study the inequality $limsup{Ax} ≤ limsup{x}.$ Recently Fridy Orhan [6] have considered some variants of this by replacing $limsup{x}$ with statistical limit superior $st - limsup{x}$. In present paper we examine similar type inequalities employing power series method $P$; non-matri...

Then, the limit points of the sequence of plays are correlated equilibria. In fact, for each correlated equilibrium there is some calibrated learning rule that the players can use which results in their playing this correlated equilibrium in the limit. Thus, the statistical concept of a calibration is strongly related to the game theoretic concept of correlated equilibrium. Journal of Economic ...

We show that the symmetry breaking of the electronic structure configurations at the large-D limit is completely analogous to the standard phase transitions and critical phenomena in statistical mechanics. Electronic structure at the large-D limit exhibits critical points with mean field critical exponents (b ­ 1 2 , a ­ 0dis, d ­ 3, and g ­ 1). The complete mapping is presented for the Hartree...

We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent’s payoff is the sum of the payoffs coming from pairwise interactions with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynam...