The present contribution deals with the numerical modeling of railway track-supporting systems-using coupled finite-infinite elements-to represent the near and distant field stress distribution, and also employing a thin layer interface element to account for the interfacial behavior between sleepers and ballast. To simulate the relative debonding, slipping and crushing at the contact area betw...

For an element x of a ring R, let A (x), Ar(x), and A(x) denote, respectively, the left, right and two-sided annihilator of x in R. For a set X , we denote cardX by |X|; and say that a subset Y of X is large in X if |Y | = |X|. We prove that if x is any nilpotent element and I is any infinite ideal of R, then A(x) ∩ I is large in I , and in particular |A (x)| = |Ar(x)| = |A(x)| = |R|. The last ...

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

Abstract-An alternating method, in conjunction with the finite element method and a solution for multiple coplanar elliptical cracks in an intinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The solution technique for multiple cracks in an infinite body has recently been developed by the prese.nt authors which implemen...

Problem 1. Infinite Products and Coproducts in Ab. We have seen that finite products and coproducts agree in Ab. However, the same is not true for infinite products and coproducts. Let I be a set and let {Ai}i∈I be a family of abelian groups, each equal to some fixed group A. (a) Show that the set AI := HomSet(I, A) is an abelian group. Furthermore, show that we can think of this group as the i...

In the automotive industry, predicting noise during design cycle is a necessary step. Well-known methods exist to answer this issue in low frequency domain. Among these, Finite Element Methods, adapted to closed domains, are quite easy to implement whereas Boundary Element Methods are more adapted to infinite domains, but may induce singularity problems. In this article, the described method, t...

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

In this paper we present error estimates for the finite element approximation of linear elliptic problems in unbounded domains that are outside an obstacle and a semi-infinite strip in the plane. The finite element approximation is formulated on a bounded domain using a nonlocal approximate artificial boundary condition. In fact there is a family of approximate boundary conditions with increasi...