ar X iv : m at h . G M / 0 50 13 73 v 1 2 2 Ja n 20 05 DIRECT DECOMPOSITIONS OF NON - ALGEBRAIC COMPLETE LATTICES

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : m at h / 05 01 43 6 v 1 [ m at h . G M ] 2 5 Ja n 20 05 TENSOR PRODUCTS OF SEMILATTICES WITH ZERO , REVISITED

Let A and B be lattices with zero. The classical tensor product, A ⊗ B, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We define a very natural condition: A ⊗ B is capped (that is, every element is a finite union of pure tensors) under which the tensor product is always a lattice. Let Conc L denote the join-semilattice with zero of c...

ar X iv : m at h / 05 01 14 5 v 1 [ m at h . D S ] 1 0 Ja n 20 05 WAVELET CONSTRUCTIONS IN NON - LINEAR DYNAMICS

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L 2-martingales which have wavelet bases.

ar X iv : m at h / 05 01 45 4 v 1 [ m at h . A G ] 2 5 Ja n 20 05 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES

We calculate the dimension of the locus of elliptic surfaces over P 1 with a section and a given Picard number, in the corresponding moduli space.

ar X iv : m at h / 05 01 55 6 v 1 [ m at h . D G ] 3 1 Ja n 20 05 Geometric Algebras

This is the first paper in a series of three where we develope a systematic approach to the geometric algebras of multivectors and ex-tensors. The series is followed by another one where those algebraic concepts are used in a novel presentation of the differential geometry of (smooth) manifolds of arbitrary global topology. The key calcu-lational tool in our program is the euclidean geometrical...