We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms h...

Many numerical methods have been developed for the solution of Poisson and Laplace equations such as finite-difference methods, finite-element methods, boundary-element methods, etc. Sinc numerical methods developed recently by Stenger and co-workers excel over other methods for problems involving singularities, infinite or semi-infinite domains as well as boundary layer behaviors. In this pape...

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we consider here are space, infinite slab, inf...

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy, and it is particularly useful when solving problems in unbounded domains. Three main aspects are consi...

Usually, systems properties are defined in terms of the infinite executions which satisfy it. In this work we explore what happens if we allow finite executions in properties definitions. In particular, we give a topological interpretation of the safety/liveness classification in the domains of: only finite, only infinite and mixed executions. Then we extend our reasoning to hyperproperties, na...

In the theory of abstract interpretation, narrowing operators are used to improve the precision of the analysis after a post-fixpoint has been reached. This is especially true on numerical domains, since they are generally endowed with infinite descending chains which may lead to a non-terminating analysis in the absence of narrowing. We provide an abstract semantics which improves the analysis...

In this paper, we show decidabil i ty of a rather expressive fragment of the situation calculus. We allow second order quantif ication over finite and inf inite sets of situations. We do not impose a domain closure assumption on actions; therefore, infinite and even uncountable domains are allowed. The decision procedure is based on automata accepting infinite trees.