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We show that two surjectiveλ-adic Galois representations which areλ-adically close near the supersingular primes are equivalent up to a twist and a standard automorphism ofGLn. In particular, two elliptic curves over a number field which are locally twist of each other in fact differ by a global twist. The proof depends on determining the automorphisms ofPGLnover a complete local ring.
An integral condition on weights u and v is given which is equivalent to the boundedness of the Hardy operator __Mens Nike Free Trainer 5.0__ between the weighted Lebesgue spaces Lup and Lvq with 0 < q < 1 < p < ∞. The Hardy inequalities are applied to give easily verified weight conditions which imply inequalities of Opial type.
We propose a stochastic differential equation approach Nike Free 3.0 V5 to principal component analysis. We give the equations governing the spectrum of the square BTB of a n×p matrix of independent Brownian motions. We apply this result to P.C.A. of perturbed continuous data.
In this paper we prove the inheritance of polynomial identities by covers of nondegenerate Jordan algebras satisfying certain ideal absorption properties. As a consequence we obtain the inheritance of speciality by Martindale-like covers, proving, in particular, that a Jordan algebra having a nondegenerate essential ideal which is special must be special.