An interpolation problem in the Denjoy–Carleman classes

Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on [a,b]subset of R$[a,b]\subset {\mathbb {R}}$ and given an increasing divergent sequence dn$d_n$ of positive integers such that the derivative of order dn$d_n$ of f has a growth of the type Mdn$M_{d_n}$, when can we deduce that f is a function in the Denjoy-Carleman class CM([a,b])C<^>M([a,b])? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence dn$d_n$ is needed

Effects of feeding raw or extruded linseed on the ruminal ecosystem of sheep

Polyunsaturated fatty acids affect bacterial and protozoal population, inducing important modifications in rumen metabolism. The aim of this study was to investigate the effect of linseed extrusion on in situ ruminal degradability and microbial number and distribution. Six ruminally fistulated sheep were divided in 3 groups and fed one of the following diets according to a replicated Latin square design: (a) control, based on mixed hay and maize grains; (b) as in (a) plus 130 g of grounded raw linseed; (c) as in (b) except that the linseed was extruded. Extrusion decreased linseed dry matter and fat degradabilities. There was a marked reduction of total protozoal population in sheep fed supplemented diets. No effects were observed between groups on bacterial concentration, hay dry matter and NDF in situ degradabilities

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity

When the chest is clueless, look downstairs

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On the Cauchy Problem for a Class of Linear Weakly Hyperbolic Operators

We study a class of linear weakly hyperbolic operators with anisotropic degeneracy on their characteristic manifold and we give sufficient conditions for the well-posedness of the related Cauchy problem