Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
Differentiability of solutions with respect to the delay function in functional differential equations
In this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differentiability result, we give a numerical study to estimate the time delay function using the quasilinearization method.
Prophets praying for, or preying on people’s faith: A reflection on prophetic ministry in the South African context
In mainline churches, the ministry of prophecy or the prophetic ministry involves the proclamation of the gospel. This, in turn, is related to the every-believer ministry. However, there is now a resurgence of the prophetic ministry as a special office as evidenced by the establishment of neo-prophetic churches. This article argues that neo-prophetic churches are tapping into people’s longing for the fresh divine word to speak directly into their personal situations. The article also probes whether neo-prophets in the prophetic activities are not also preying on people’s faith.