ar X iv : m at h / 02 08 08 7 v 1 [ m at h . O A ] 1 1 A ug 2 00 2 WHEN ARE CROSSED PRODUCTS BY MINIMAL DIFFEOMORPHISMS ISOMORPHIC ?

ar X iv : m at h / 02 08 19 7 v 1 [ m at h . D G ] 2 6 A ug 2 00 2 Hyperbolic Rank of Products

Generalizing [BrFa] we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1 +m2 −1 in the product X := Xm1 1 ×X m2 2 of two Hadamard manifolds Xmi i of dimension mi with pinched negative curvature. Combining this result with [BuySch] we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.

ar X iv : m at h / 06 08 16 3 v 1 [ m at h . L O ] 7 A ug 2 00 6 IND - AND PRO - DEFINABLE SETS

We describe the indand procategories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.

ar X iv : m at h / 05 08 20 7 v 1 [ m at h . R A ] 1 1 A ug 2 00 5 ON DETERMINING MINIMAL SPECTRALLY ARBITRARY PATTERNS

In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [3]. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.

ar X iv : m at h / 05 08 29 7 v 1 [ m at h . ST ] 1 6 A ug 2 00 5 CONVERGENCE OF ESTIMATORS IN LLS ANALYSIS

We establish necessary and sufficient conditions for consistency of estimators of mixing distribution in linear latent structure analysis.

ar X iv : m at h / 06 08 37 7 v 1 [ m at h . R T ] 1 5 A ug 2 00 6 ALGEBRAS OF DERIVED DIMENSION ZERO