This paper introduces some elementary notions in Measure-Theoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers. Finally, the notions of conditional expectation and conditional probability are introduced. 1 Heuristic Introduction Probability theory is concerned with...

dynamic game theory is applied to analyze the timber market in northern iran as a duopsony. the nash equilibrium and the dynamic properties of the system based on marginal adjustments are determined. when timber is sold, the different mills use mixed strategies to give sealed bids. it is found that the decision probability combination of the different mills follow a special form of attractor an...

A new approach to studying active suspensions is presented. They exhibit a specific behavior pattern, sometimes referred as turbulence. Starting from first principles, we establish description for an suspension, consisting of Newtonian fluid and Janus particles. The phase described by Navier–Stokes equations the particles Newton–Euler equations. level set used separate two phases, well-known re...