Let E = ((eij))n×n be a fixed array of real numbers such that eij = eji, eii = 0 for 1 ≤ i, j ≤ n. Let the symmetric group be denoted by Sn and the collection of involutions with no fixed points by Πn, that is, Πn = {π ∈ Sn : π 2 = id, π(i) 6= i∀i}. For π uniformly chosen from Πn, let YE = Pn i=1 eiπ(i) and W = (YE − μE)/σE where μE = E(YE) and σ 2 E = Var(YE). Denoting by FW and Φ the distribu...

Baker's yeast suspensions having bacterial populations of 10(6) and 10(8) CFU/ml were subjected to autolysis processes designed to obtain yeast extracts (YE). The bacterial contaminants added to the yeast cell suspensions were produced with spent broths obtained from a commercial yeast production plant and contained 59% cocci (Leuconostoc, Aerococcus, Lactococcus) as well as 41% bacilli (Bacill...

Let G(xr − xe) be the causal Green function for the wave equation in four spacetime dimensions, representing the signal received at the spacetime point xr due to an impulse emitted at the spacetime point xe. Such emission and reception processes are highly idealized, since no signal can be emitted or received at a single (mathematical) point in space and time. We present a simple model for exte...

teaching the grammatical tenses is considered to be one of the most controversial challenges among teachers and researchers in teaching persian language to non-persian speakers. prioritizing the tenses in accordance with their frequency could greatly facilitate the process of language learning. in this research, a comparison has been made between the frequency of the tenses in spoken and writte...

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