منابع مشابه
Unfolding Polynomial Maps at Infinity
Let f : Cn → C be a polynomial map. The polynomial describes a family of complex affine hypersurfaces f−1(c), c ∈ C. The family is locally trivial, so the hypersurfaces have constant topology, except at finitely many irregular fibers f−1(c) whose topology may differ from the generic or regular fiber of f . We would like to give a full description of the topology of this family in terms of easil...
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Let R be a real closed field and A = R[x1, . . . , xn]. Let Sper A denote the real spectrum of A. There are two kinds of points in Sper A: finite points (those for which all of |x1|,. . . ,|xn| are bounded above by some constant in R) and points at infinity. In this paper we study the structure of the set of points at infinity of Sper A and their associated valuations. Let T be a subset of {1, ...
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In this paper we study necessary optimality conditions for the optimization problem infimumf0(x) subject to x ∈ S, where f0 : R → R is a polynomial function and S ⊂ R is a set defined by polynomial inequalities. Assume that the problem is bounded below and has the Mangasarian– Fromovitz property at infinity. We first show that if the problem does not have an optimal solution, then a version at ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2011
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-011-0128-5