An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Temporal structure and enablement representation for mutual wills: A Petri net approach

Those temporal formalisms that are sporadically found nowadays in the literature of AI & Law are based on temporal logic. We claim a revived role for another major class of temporal representation: Petri nets. This formalism, popular in computing from the 1970s, had its potential recognized on occasion in the literature of legal computing as well, but apparently the discipline has lost sight of it, and its practitioners on average need be tutored into this kind of representation. Asynchronous, concurrent processes—for which the approach is well‐suited—are found in the legal domain, in disparate contexts. We develop an example for Mutual Wills.