Doğan Çömez

Weighted ergodic theorems for mean ergodic ₁-contractions

It is shown that any bounded weight sequence which is good for all probability preserving transformations (a universally good weight) is also a good weight for any L1-contraction with mean ergodic (ME) modulus, and for any positive contraction of Lp with 1 < p < ∞. We extend the return times theorem by proving that if S is a Dunford-Schwartz operator (not necessarily positive) on a Lebesgue space, then for any g bounded measurable {Sng(ω)} is a universally good weight for a.e. ω. We prove that if a bounded sequence has ”Fourier coefficents”, then its weighted averages for any L1-contraction with mean ergodic modulus converge in L1-norm. In order to produce weights, good for weighted ergodic theorems for L1-contractions with quasi-ME modulus (i.e., so that the modulus has a positive fixed point supported on its conservative part), we show that the modulus of the tensor product of L1contractions is the product of their moduli, and that the tensor product of positive quasi-ME L1-contractions is quasi-ME.

Steady-state skill levels of workers in learning and forgetting environments: A dynamical system analysis

This article presents a study on the long-term (i.e., steady-state, convergence) characteristics of workers’ skill levels under learning and forgetting in processing units in a manufacturing environment, in which products are produced in batches. Assuming that all workers already have the basic knowledge to execute the jobs, workers learn (accumulate their skill) while producing units within a batch, forget during interruptions in production, and relearn when production resumes. The convergence properties in the paper are examined under assumptions of an infinite time horizon, a constant demand rate, and a fixed lot size. Our work extends the steady-state results of Teyarachakul, Chand, and Ward (2008) to the learning and forgetting functions that belong to a large class of functions possessing some differentiability conditions. We also discuss circumstances of manufacturing environments where our results would provide useful managerial information and other potential applications.