Abstract Tailings transport system design is generally based on identifying the minimum and maximum process boundary conditions for pump selection pipeline sizing. The approach robust well-proven. However, has potential to skew selections operating scenarios that have a very low likelihood of occurring, such as combination high solids throughput tailings concentration. can result in overly cons...

Previously in class we proved that if we color the edges of K6 using blue or red color, then either there is a blue K3 or a red K3 as a subgraph. Here Kn is the complete graph (every pair of vertices are connected) on n vertices. We can generalize the above concept and ask, are there complete graphs for which any 2-coloring gives rise to either a blue Kk or a red Kl. It has been shown that ther...

In this chapter, we discuss mathematical methods to analyze problems involving uncertainty. Such problems arise naturally in many fields including economics, finance, biology, medical decision making and operations research. Probability and stochastic processes are useful mathematical tools for that purpose. This article explains useful notions of probability and stochastic processes with typic...

Remark. This is also known as the Lubell-Yamamoto-Meshalkin inequality. Solution: Generate a random permutation σ = (x1, . . . , xM ) of [M ]. Let each Ei be the event that the set Ai appears as the initial segment of σ, i.e., that {x1, . . . , xai} = Ai. Since none of the Ai contain each other, the Ei are mutually exclusive. But each P [Ei] = ( M ai )−1 , so the LHS is P [∪Ei], and probabiliti...

In 1947 Paul Erdös [8] began what is now called the probabilistic method. He showed that if (fc)2 ' ' < i then there exists a graph G on n vertices with clique number u)(G) < k and independence number ct(G) < k. (In terms of the Ramsey function, R(k,k) > n.) In modern language he considered the random graph G(n, .5) as described below. For each fc-set S let Bs denote the "bad" event that S is e...