Exact Discretization of Harmonic Tensors

Exact discretization of harmonic tensors

Furstenberg [7] and Lyons and Sullivan [14] have shown how to discretize harmonic functions on a Riemannian manifold M whose Brownian motion satisfies a certain recurrence property called ∗-recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, under certain restrictions on the holonomy of the connection,...

On the exact discretization of the classical harmonic oscillator equation

We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical applications. MSC 2000: 39A10; 65L12; 37M05; 65P10; 34K28

A Combinatorial Note for Harmonic Tensors

Hardy-Littlewood Theorems for A-Harmonic Tensors

Exact relations for effective tensors of polycrystals. I: Necessary conditions

The set of all effective moduli of a polycrystal usually has a nonempty interior. When it does not, we say that there is an exact relation for effective moduli. This can indeed happen as evidenced by recent results [4, 10, 12] on polycrystals. In this paper we describe a general method for finding such relations for effective moduli of laminates. The method is applicable to any physical setting...