Sums with curves
نویسندگان
چکیده
منابع مشابه
Sums of Squares on Reducible Real Curves
We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we show how the answer depends on the configuration of the irreducible components and give complete necessary and sufficient conditions. We also prov...
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Given an affine algebraic variety V over R with compact set V (R) of real points, and a non-negative polynomial function f ∈ R[V ] with finitely many real zeros, we establish a local-global criterion for f to be a sum of squares in R[V ]. We then specialize to the case where V is a curve. The notion of virtual compactness is introduced, and it is shown that in the localglobal principle, compact...
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This paper discusses the problem of testing the equality of two nonparametric autoregressive functions against two-sided alternatives. The heteroscedastic error and stationary densities of the two independent strong mixing strictly stationary time series can be possibly different. The paper adapts the partial sum process idea used in the independent observations settings to construct the tests ...
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In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lower bounds for linear forms in logarithms. Its main virtue is that it enables us to carry out such a program explicitly, a...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1984
ISSN: 0022-247X
DOI: 10.1016/0022-247x(84)90012-x