An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems...

Coupled finite-infinite element computations are very efficient for modeling large scale acoustics problems. Parallel algorithms, like sub-structuring and domain decomposition methods, have shown to be very efficient for solving huge linear systems arising from acoustics. In this paper, a coupled finite-infinite element method is described, formulated and analyzed for parallel computations purp...

Let δ0(P, k) denote the degree k dilation of a point set P in the domain of plane geometric spanners. If Λ is the infinite square lattice, it is shown that 1+ √ 2 ≤ δ0(Λ, 3) ≤ (3+2 √ 2) 5−1/2 = 2.6065 . . . and δ0(Λ, 4) = √ 2. If Λ is the infinite hexagonal lattice, it is shown that δ0(Λ, 3) = 1 + √ 3 and δ0(Λ, 4) = 2. All our constructions are planar lattice tilings constrained to degree 3 or 4.

We show in this paper that every domain in a separable Hilbert space, say H, which has a C smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Kr...