This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which a generalization of recently proposed index, where γ any real number. For connected graph G more than two vertices, number ABSγ(G) defined as sum (1−2(dx+dy)−1)γ over all edges xy G, dx and dy represent degrees vertices x y respectively. −10≤γ≤10, significance ABSγ examined on data set twenty-five benzenoid hy...

In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, i...

In this lecture we study basic solution concepts in game theory, namely the notion of dominant strategy and Nash equilibrium. We consider rational players in a competitive environment. A rational player is a player with priorities (or utility) that tries to maximize the utility (or minimize cost) while considering that other players are also rational. A competitive environment is an environment...

We describe a method for an agent playing a generalsum normal form game to balance the rewards of exploiting a prediction of opponent behavior with the risks of being exploited by a self-interested opponent while guaranteeing a worst-case safety margin. Our algorithm, Restricted Stackelberg Response with Safety, calculates a probability distribution over the agent’s moves that balances those co...

This paper provides a novel approach to multi-agent coordination in general sum Markov games. Contrary to what is common in multi-agent learning, our approach does not focus on reaching a particular equilibrium between agent policies. Instead, it learns a basis set of special joint agent policies, over which it can randomize to build different solutions. The main idea is to tackle a Markov game...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...