ar X iv : m at h / 05 08 55 9 v 3 [ m at h . C A ] 2 J un 2 00 6 RELAXATION THEOREMS IN NONLINEAR ELASTICITY

ar X iv : m at h / 05 08 55 9 v 1 [ m at h . C A ] 2 9 A ug 2 00 5 RELAXATION THEOREMS IN NONLINEAR ELASTICITY

where detξ denotes the determinant of ξ, and (C4) W (PξQ) = W (ξ) for all ξ ∈ M and all P,Q ∈ SO(3) for N = 3, with SO(3) := {Q ∈ M : QQ = QQ = I3 and detQ = 1}, where I3 denotes the identity matrix in M 3×3 and Q is the transposed matrix of Q. (In fact, (C4) is an additional condition which is not related to (2). However, it means that W is frame-indifferent, i.e., W (Pξ) = W (ξ) for all ξ ∈ M...

ar X iv : m at h / 05 08 55 9 v 2 [ m at h . C A ] 3 0 A ug 2 00 5 RELAXATION THEOREMS IN NONLINEAR ELASTICITY

where detξ denotes the determinant of ξ, and (C4) W (PξQ) = W (ξ) for all ξ ∈ M and all P,Q ∈ SO(3) for N = 3, with SO(3) := {Q ∈ M : QQ = QQ = I3 and detQ = 1}, where I3 denotes the identity matrix in M 3×3 and Q is the transposed matrix of Q. (In fact, (C4) is an additional condition which is not related to (2). However, it means that W is frame-indifferent, i.e., W (Pξ) = W (ξ) for all ξ ∈ M...

ar X iv : h ep - p h / 06 08 05 0 v 1 4 A ug 2 00 6 Percolation and high energy cosmic rays above 10 17 eV

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 / 03 05 20 7 v 4 [ m at h . D S ] 6 M ay 2 00 6 Lipschitz Flow - box Theorem

A generalization of the Flow-box Theorem is proven. The assumption of a C vector field f is relaxed to the condition that f be locally Lipschitz. The theorem holds in any Banach space.