An object-oriented numerical integration template implementation is presented on the basis of the CCC programming language. Aiming its straightforward application in finite and boundary element methods, the design supports integrand objects of scalar, vector or matrix types, so that a single programming statement is able to integrate element matrices and vectors. The integrand can contain singu...

We show that standard Einstein gravity coupled to a free conformal field theory (CFT) in Anti de Sitter space can undergo a Higgs phenomenon whereby the graviton acquires a nonzero mass (and three extra polarizations). We show that the essential ingredients of this mechanism are the discreteness of the energy spectrum in AdS space, and unusual boundary conditions on the elementary fields of the...

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly nonorientable) surface of genus g ≥ 0 with b ≥ 0 boundaries is O(g + b). So far, the result was known only f...

In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...

It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbolic leaves: they are amenable if and only if they are elementary in the sense that one can assign (in a measurable way) to any leaf a finite subset of its hyperbolic boundary (as in the group case, such subsets cannot ...

This paper presents a discussion of complex shift dynamics of some elementary cellular automaton rules (rules 30, 41, and 110). Equations that show some degree of self-similarity are obtained. It is demonstrated that rules 30, 41, and 110 exhibit Bernoulli shifts and are topologically mixing on one of their own closed invariant subsystems. Furthermore, many complex Bernoulli shifts are explored...

Consider a semi-algebraic set A in R constructed from the sets which are determined by inequalities pi(x) > 0, pi(x) ≥ 0, or pi(x) = 0 for a given list of polynomials p1, . . . , pm. We prove several statements that fit into the following template. Assume that in a neighborhood of a boundary point the semi-algebraic set A can be described by an irreducible polynomial f . Then f is a factor of a...

The equation studied is u00+ n 1 r u 0+ "u u0 = 0; with boundary conditions u (1) = 0; u (1) = 1. This model equation has been studied by many authors since it was introduced in the 1950s by P. A. Lagerstrom. We use an elementary approach to show that there is an in nite series solution which is uniformly convergent on 1 r < 1: The rst few terms are easily derived, from which one quickly deduce...