4,877 research outputs found
Strong nonnegativity and sums of squares on real varieties
Motivated by scheme theory, we introduce strong nonnegativity on real
varieties, which has the property that a sum of squares is strongly
nonnegative. We show that this algebraic property is equivalent to
nonnegativity for nonsingular real varieties. Moreover, for singular varieties,
we reprove and generalize obstructions of Gouveia and Netzer to the convergence
of the theta body hierarchy of convex bodies approximating the convex hull of a
real variety.Comment: 11 pages, 4 figure
On Permutation Binomials over Finite Fields
Let be the finite field of characteristic containing elements and a binomial with coefficients in
this field. If some conditions on the gcd of an are satisfied then
this polynomial does not permute the elements of the field. We prove in
particular that if permutes , where
and , then , where , and that this bound of in term of only, is sharp. We
show as well how to obtain in certain cases a permutation binomial over a
subfield of from a permutation binomial over
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