Out of Equilibrium Correlations in the XY Chain

We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast.     

The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

Best affine unbiased representations of the fully restricted general Gauss-Markov model

This article completes and simplifies earlier results on the derivation of best linear, or affine, unbiased estimates in the general Gauss-Markov model with a singular dispersion matrix and additional restrictions under very general conditions. We provide the class of all linear representations of the best affine unbiased estimator with precise statements concerning its indeterminacy.     

TheK-admissibility of 2A 6 and 2A 7

LetK be a field and letG be a finite group.G isK-admissible if there exists a Galois extensionL ofK withG=Gal(L/K) such thatL is a maximal subfield of a centralK-division algebra. This paper contains a characterization of those number fields which areQ ₁₆-admissible. This is the same class of number fields which are 2A ₆=SL(2, 9) and 2A ₇ admissible. Dedicated to John Thompson to celebrate his Wolf Prize in Mathematics 1992