A proof of Schur's conjecture and an improvement.
It is assumed that activity times in stochastic activity networks (SANs) are independent Erlang random variable (r.v.). A recurrence method of determining the th moments of the completion time is presented. Applications are provided for illustration and are used to evaluate the applicability and appropriateness of the Erlang model to represent activity network.
There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers...